makarytchev-gdz-8-2001 только 1-677 (988796), страница 9

Просмтор этого файла доступен только зарегистрированным пользователям. Но у нас супер быстрая регистрация: достаточно только электронной почты!

Текст из файла (страница 9)

Квадратный корень из степени№384а)(0,1)2б)(−0,4)2= −0,4 = 0,4 ;в)(−0,8)2= −0,8 = 0,8;г)(1,7)2д)(−19)2е)242 = 24 = 24;= 0,1 = 0,1 ;= 1,7 = 1,7;= −19 = 19;ж) 2 (−23) = 2 ⋅ −23 = 2 ⋅ 23 = 46;2з) 5 522 = 5 ⋅ 52 = 5 ⋅ 52 = 260;и) 0,2 (−61) = 0,2 ⋅ −61 = 0,2 ⋅ 61 = 12,2.2№385а) подставим x = 22: x 2 = 222 = 22 = 22;подставим x = −35: x 2 = ( −35) 2 = −35 = 35;23232подставим x = −1 : x 2 =  −1  = −122=1 ;33подставим x = 0: x 2 = 02 = 0 = 0;б) подставим a = −7:2 a 2 = 2 (−7) = 2 ⋅ −7 = 2 ⋅ 7 = 14;2подставим a = 12:2 a 2 = 2 122 = 2 ⋅ 12 = 2 ⋅ 12 = 24;в) подставим y = −15: 0,1 y 2 = 0,1 (−15) = 0,1 ⋅ −15 = 0,1 ⋅ 15 = 1,5 ;2подставим y = 27: 0,1 y 2 = 0,1 272 = 0,1 ⋅ 27 = 0,1 ⋅ 27 = 2,7 .№386а)p2 = p ;б)y2 = y ;в) 3 b2 = 3 b ;г) −0,2 x 2 = −0,2 x ;д)25a 2 = 5 ⋅ a 2 = 5 ⋅ a .№387а)a 2 = a = a , если a>0;б)n2 = n = − n, если n<0;в) 3 c2 = 3 ⋅ c = 3c, если с>0;3 c2 = 3 ⋅ c = 3 ⋅ 0 = 0, если с=0;г) −5 y 2 = −5 ⋅ y = −5 y, если y>0;д)36 x 2 = 6 x = 6 ⋅ x = −6 x , если х<0;36 x 2 = 6 x = 6 ⋅ 0 = 6 ⋅ 0 = 0;е) − 9 y 2 = −3 ⋅ y = −3( − y ) = 3 y , если y<0;ж) −5 4 x 2 = −5 ⋅ 2 x = −5 ⋅ 2 x = −10 x, если х>0;−5 4 x 2 = − − 10 x = −10 ⋅ 0 = 0, если х=0;з) 0,5 16a 2 = 0,5 ⋅ 4a = 0,5 ⋅ (− a ) = −2a , если а<0.№338а) 2 m2 = 2 m = 2m, при m≥0;б) −3 a 2 = −3 a = −3a, при a>0;в)0,64 x 2 = 0,8 ⋅ x = 0,8(− x ) = 0,8 x , при x≤0;г) − 0,25 y 2 = − 0,5 y = −0,5 ⋅ − y = 0,5 y , при у<0.№389а)y 6 = y 3 = y 3 , если у≥0;б)m4 = m2 = m2 ;в)x 6 = x 3 = − x 3 , если x<0;г) 5 a8 = 5 a 4 = 5a 4 ;д)1 12 1 6 1 6c = c = c ;333( )е) 1,5 t 14 = 1,5 t 7 = 1,5 ⋅ − t 7 = −1,5t 7 , если t<0.№390а)0,49 x18 = 0,7 x 9 = 0,7 x 9 , при x<0;б)0,01a 26 = 0,1a13 = 0,1a13; при а>0;0,01a 26 == 0,1a13 = 0, при а=0;в) 15 0,16c12 = 15 ⋅ 0,4c6 = 15 ⋅ 0,4c6 = 6c6 ;г) 0,8 100 y16 = 0,8 ⋅ 10 y8 = 8 y8 .№391а)p10 = p5 , при р>0;б)x18 = x 9 = − x 9 , при х<0;в)y12 = y 6 = y 6 ;г) 15 b16 = 15 ⋅ b8 = 15b8 ;д) 1,6 x8 = 1,6 ⋅ x 4 = 1,6 x 4 ;( )е) 0,1 a 6 = 0,1 ⋅ a 3 = 0,1 ⋅ − a 3 = −0,1a 3 , при а<0;№392а)24 = 22 = 4;б)34 = 32 = 9;в)2 6 = 23 = 8 ;г)108 − 104 ;д)(−5)4= (−5) = 25;е)(−2)8= (−2) = 16;ж)34 ⋅ 52 = 32 ⋅ 5 = 45;з)2426 ⋅ 27 = 27 ⋅ 72 = 8 ⋅ 49 = 392.№393а)114 = 112 = 121;б)46 = 43 = 64 = 64;в)(−3)8= (−3) = 81 = 81;г)(−6)4= (−6) = 36;д)28 ⋅ 32 = 24 ⋅ 3 = 48;е)34 ⋅ 56 = 32 ⋅ 53 = 9 ⋅ 125 = 1125;ж)72 ⋅ 24 7 ⋅ 24 = 7 ⋅ 24 = 112;з)36 ⋅ 54 = 33 ⋅ 52 = 27 ⋅ 25 = 675.42№394а)20736 = 28 ⋅ 34 = 24 ⋅ 32 = 24 ⋅ 32 = 16 ⋅ 9 = 144;б)50625 = 34 ⋅ 54 = 32 ⋅ 52 = 9 ⋅ 25 = 225;в)28224 = 26 ⋅ 32 ⋅ 72 = 23 ⋅ 3 ⋅ 7 = 8 ⋅ 3 ⋅ 7 = 168;г)680625 32 ⋅ 54 ⋅ 112 = 3 ⋅ 52 ⋅ 11 = 3 ⋅ 2511 = 825.№395а)2304 = 28 ⋅ 32 = 24 ⋅ 3 = 24 ⋅ 3 = 16 ⋅ 3 = 48;б)18225 = 36 ⋅ 52 = 33 ⋅ 5 = 27 ⋅ 5 = 135;в)254016 26 ⋅ 34 ⋅ 72 = 23 ⋅ 32 ⋅ 7 = 8 ⋅ 9 ⋅ 7 = 504.УПРАЖНЕНИЯ ДЛЯ ПОВТОРЕНИЯ№39736  a +1 5−+ 2 ⋅= a + 1 a − 1 a − 1 2 a +1 536 ⋅−+= a + 1 a − 1 (a + 1)(a − 1)  2= =5(a − 1) − 3( a + 1) + 6 a + 1 5a − 5 − 3a − 3 + 6 a + 1⋅=⋅=(a + 1)( a − 1)2(a + 1)(a − 1)2=2a − 2a + 1 2(a − 1)(a + 1)⋅== 1, что не зависит от а.( a + 1)(a − 1) 22(a + 1)( a − 1)№ 398.x  x 2 − 25 x+5− 2= 2⋅5 x − 5 x x − 25  x+5 ( x − 5 )( x + 5 )x ⋅= −=−−+x(x5)(x5)(x5)5x 2 + 10 x + 25 − x 2 ( x − 5 )( x + 5 ) 5( 2 x + 5 ) 2 x + 5=⋅==.x( x − 5 )( x + 5 )55xx№ 399.На рисунке буквами а, b и c обозначены графики функций:y8bа64202468-4-6-8а – график функции y = 2 x + 2;b – график функции y = −2 x + 2;x4с – график в функции y = − − 3 .№ 400.Из условия задачи имеем:cV = πR2H; R2 =V;R=πHV.πH§ 7.

Применение свойств арифметическогоквадратного корня17. Вынесение множителя из-под знака корня. Внесениемножителя под знак корня№ 401.а) 12 = 4 ⋅ 3 = 4 ⋅ 3 = 2 3 ;б) 18 = 9 ⋅ 2 = 9 ⋅ 2 = 3 2 ;в)80 = 16 ⋅ 5 = 16 ⋅ 5 = 4 5 ;г)48 = 16 ⋅ 3 = 16 ⋅ 3 = 4 3 ;д) 125 = 25 ⋅ 5 = 25 ⋅ 5 = 5 5 ;е) 108 = 27 ⋅ 4 = 27 ⋅ 4 = 3 3 ⋅ 2 = 6 3 ;ж)363 = 3 ⋅ 121 = 121 ⋅ 3 = 11 3 ;з)845 = 5 ⋅ 169 = 169 ⋅ 5 = 13 5 .№ 402.111124 =4⋅6 =4 ⋅ 6 = ⋅2 6 = 6 ;2222222б)45 =9⋅5 = ⋅3 5 = 2 5 ;333111в) −147 = −49 ⋅ 3 = − ⋅ 7 3 = − 3 ;7771111г) −275 = −25 ⋅ 11 = −25 ⋅ 11 = − ⋅ 5 11 = − 11 ;5555а)д) 0,1 20000 = 0,1 10000 ⋅ 2 = 0,1 ⋅ 100 2 = 10 2 ;е) − 0,05 28800 = −0,05 2 5 ⋅ 3 2 ⋅ 10 2 = −0,05 ⋅ 2 2 ⋅ 3 ⋅ 10 2 == −0,05 ⋅ 120 2 = −6 2 .№ 403.а)20 = 4 ⋅ 5 = 2 5 ;б)98 = 49 ⋅ 2 = 49 ⋅ 2 = 7 2 ;в)200 = 100 ⋅ 2 = 10 2 ;г) 160 = 16 ⋅ 10 = 16 ⋅ 10 = 4 10 ;д) 0,2 75 = 0,2 3 ⋅ 25 = 0,2 3 ⋅ 25 = 0,2 ⋅ 5 3 = 3 ;е) 0,7 300 = 0,7 3 ⋅ 100 = 0,7 ⋅ 10 3 = 7 3 ;ж) − 0,125 192 = −0,125 16 ⋅ 3 ⋅ 2 ⋅ 2 = −0,125 16 ⋅ 2 2 ⋅ 3 == −0,125 ⋅ 4 ⋅ 2 3 = − 3 ;111з) −450 = −9 ⋅ 5 ⋅ 10 = − ⋅ 3 ⋅ 5 2 = −5 2 ;333и) − 10 0,02 = −1 ⋅ 10 0,02 = − 100 ⋅ 0,02 = − 2 ;к) 5л) −aa= 125 ⋅=5525a= 5a ;511112 x = −1 ⋅12 x = −⋅ 12 x = − 3 x .224№ 404.а) 7 10 = 49 ⋅ 10 = 490 ;б) 5 3 = 25 ⋅ 3 = 75 ;в) 6 x = 36 ⋅ x = 36 x ;г) 10 y = 100 ⋅ y = 100 y ;д) 3 2a = 9 ⋅ 2a = 18a ;е) 5 3b = 25 ⋅ 3b = 75b .№ 405.а) − 2 3 = − 4 ⋅ 3 = − 12 ;б) − 3 5 = − 9 ⋅ 5 = − 45 ;в) − 7 a = − 49 ⋅ a = − 49a ;г) − 0,2 b = − 0,04 ⋅ b = − 0,04b .№ 406.а) 311= 9⋅=339= 3;3б) 233= 4⋅=443⋅ 4= 3;4в)118 =31⋅ 18 = 2 ;9г) − 10 0,02 = − 100 ⋅ 0,02 = − 2 ;д) 5е) −99= 25 ⋅= 45 ;551112 x = −⋅ 12 x = − 3x .24№ 407.а) 2 2 = 4 ⋅ 2 = 8 ;б) 5 y = 25 ⋅ y = 25 y ;в) − 7 3 = − 49 ⋅ 3 = − 147 ;г) − 6 2a = − 36 ⋅ 2a = − 72a ;д)118b =311 ⋅ 18⋅ 18b =b = 2b ;99 ⋅1е) − 0 ,1 200с = − 0,1 ⋅ 200с = − 2с .№ 410.а) 3 3 = 27 ; 2 6 = 24 ;4 2 = 32 ;24 p 27 p 32 , значит,2 6 p3 3 p4 2 ;б) 6 2 = 36 ⋅ 2 = 72 ; 3 7 = 63 ;2 14 = 56 ;56 p 58 p 63 p 72 ⇒2 14 p 58 p 3 7 p 6 2 .№ 411.а)4 ⋅ 7 ∨ 49 ⋅ 2 ;б)9 ⋅ 120 ∨ 4 ⋅ 270 ;28 p 98 ; 2 7 p 7 2 ;1080 = 1080 ;3 120 p 2 270 ;в)11;⋅ 6 ∨ 36 ⋅421,5 p 18 ;636∨4211.6 p622№ 412.а)7 x 2 = 7 x = 7 x , при x ≥ 0 ;б) 10 y 2 = 10 y = 10 y , при y p 0 ;в)x3 = x ⋅ x = x x ;г)a5 = a4 ⋅ a = a a 2 = a2 a ;д) 16 y 7 = 16 y ⋅ y 6 = 4 y y 3 = 4 y 3 y ;е)x 3x3x 313x= x⋅ 3⋅ x =x=.16444№ 413.а)8a 3 = 2 2 ⋅ 2a 2 ⋅ a = 2a 2a ;б)300b 5 = 3 ⋅ 100b 4 ⋅ b = 10b 2 3b ;в)48 x 2 = 16 ⋅ 3x 2 = 4 x 3 = −4 x 3 , при x ≤ 0 ;г)72a 4 = 2 ⋅ 36a 4 = 6a 2 2 ;д)50a 7 = 2 ⋅ 25a 6 ⋅ a = 5a 2 2a ;е)27c 6 = 3 2 ⋅ 3c 6 = 3 c 3 3 = −3c 3 3 , при c p 0 .№ 414.а)6 x 2 = 6 ⋅ x = x 6 , при x ≥ 0 ;б)3 y 2 = 3 ⋅ y = − 6 y , при y p 0 ;в)9a 3 = 3 a ⋅ a = 3a a ;г)50b 4 = 2 ⋅ 25b 4 = 2 ⋅ 5b 2 = 5b 2 2 .УПРАЖНЕНИЯ ДЛЯ ПОВТОРЕНИЯ№ 415. 2x + 12x − 1  x 2 − 92x − 1  x 2 − 9 2x + 1 ⋅+ 1 = −− 2+1 = 2⋅ x − 3x x + 3x  7 x x(x − 3) x(x + 3)  7 x=(2 x + 1)(x + 3) − (x − 3)(2 x − 1) ⋅ x − 9 + 1 =7xx(x − 3)(x + 3)=2x 2 + 6x + x + 3 − 2x 2 + x + 6x − 3 x 2 − 9⋅+1 =7xx(x − 3)(x + 3)2=(x + 3)(x − 3) + 1 = 14 x + 1 = 2 + 1 = 2 + x .14 x⋅7xx(x − 3)(x + 3)x ⋅ 7xxx№ 416.Обозначим за х – количество книг, переплетенных в первый день;тогда (х + 12) – количество книг, переплетенных во второй день;также (х + х +12) – количество книг, переплетенных за первые двадня;5(x + x + 12) - количество книг, переплетенных в третий день.7Всего за три дня было переплетено 144 книги.

Получаем уравнение:x + (x + 12 ) +5(x + x + 12) = 144 ;75(2 x + 12) = 144 ;7(2 x + 12)1 + 5  = 144 ; 712(2 x + 12) = 144 ;7x+6= 6 ; x + 6 = 42 ; x = 36 ;75x + 12 = 48 ; (x + x + 12 ) = 60 .72 x + 12 +Ответ: в первый день переплели 36 книг, во второй – 48 книг, в третий – 60 книг.№ 417.4x − 1 7 5 − x 4x − 1 7  5 − x; 36 ⋅ ⋅ 36 ;+ =+ =491249 123(4 x − 1) + 9 ⋅ 7 = 4(5 − x ) ; 12 x − 3 + 63 = 20 − 4 x ;16 x = −40 ; x = −2,5 ;2 x − 9 2(5 x + 3) 1 30(2 x − 9 ) 30 ⋅ 2(5 x + 3) 1б)−= ⋅ 30 ;−= ;61526152а)5(2х – 9) – 4(5х + 3) = 15;-10х – 57 = 15;10х = - 72;х = - 7,2.18.

Преобразование выражений, содержащихквадратные корни№ 418.а) 2 x + 3 x − y = 5 x − y ;б) − 4 a + 2 b + 3 a = 2 b − a ;в)9a + 25a − 36a = 3 a + 5 a − 6 a = 2 a ;г) 16n + 25n − 9n = 4 n + 5 n − 3 n = 6 n ;д)5a − 2 20a − 3 80a = 5a − 2 4 ⋅ 5a − 3 16 ⋅ 5a == 5a − 4 5a − 12 5 = −15 5a ;е)75 + 48 − 300 = 3 ⋅ 25 + 16 ⋅ 3 − 3 ⋅ 100 == 5 3 + 4 3 − 10 3 = − 3 ;ж) 3 8 − 50 + 2 18 = 3 2 ⋅ 4 − 2 ⋅ 25 + 2 2 ⋅ 9 == 6 2 −5 2 +6 2 = 7 2 ;з)242 − 200 + 8 = 2 ⋅ 121 − 2 ⋅ 100 + 2 ⋅ 4 == 11 2 − 10 2 + 2 2 = 3 2 ;и)75 − 0,1 300 − 27 = 3 ⋅ 25 − 0,1 3 ⋅ 100 − 3 ⋅ 9 == 5 3 − 3 −3 3 = 3 ;98 − 72 + 0,5 8 = 2 ⋅ 49 − 2 ⋅ 36 + 0,5 4 ⋅ 2 =к)= 7 2 −6 2 + 2 = 2 2 .№419а) 8 p − 25 + 18 p = 2 2 p − 5 + 3 2 p = 5 2 p − 5;б)16c + 2 40c − 3 90c = 4 c + 2 ⋅ 2 10c − 3 ⋅ 3 10c = 4 c + 4 10c − 9 10c== 4 c − 5 10c;в) 5 27 − 4 48m − 2 12m = 5 3 ⋅ 9 − 4 3 ⋅16m − 2 4 ⋅ 3m == 15 3 − 16 3m − 4 3m = 15 3 − 20 3m;г) 54 − 24 + 150 = 6 ⋅ 9 − 6 ⋅ 4 + 25 ⋅ 6 == 3 5 − 2 6 + 5 6 = 6 6;д) 3 2 + 32 − 200 = 3 2 + 4 2 − 10 2 = −3 2;е) 2 72 − 50 − 2 8 = 2 2 ⋅ 36 − 2 ⋅ 4 == 2 ⋅ 6 2 − 5 2 − 2 ⋅ 2 2 = 12 2 − 5 2 − 4 2.№420( 12 + 15 ) ⋅ 3 =б) 5 (3 5 + 5 8 ) =а)= 15 + 10 10(12 ⋅ 3 + 15 ⋅ 3 = 4 ⋅ 3 ⋅ 3 + 3 ⋅ 5 ⋅ 3 = 6 + 3 5 ;5 ⋅ 3 5 + 5 5 ⋅ 8 = 3 ⋅ 5 + 5 4 ⋅10 = 15 + 5 ⋅ 2 10 =)в) 4 3 − 2 6 ⋅ 2 3 = 4 3 ⋅ 2 3 − 2 6 ⋅ 2 3 = 24 − 4 ⋅ 3 2 = 24 − 12 2;г)(35 − 2 3 ⋅ 5 + 60 = 3 5 ⋅ 5 − 2 3 ⋅ 5 + 4 ⋅15 = 3 ⋅ 5 − 2 15 + 2 15д)(=15;))28 − 2 3 + 7 ⋅ 7 + 84 == 28 ⋅ 7 − 2 3 ⋅ 7 + 7 ⋅ 7 + 21 ⋅ 4 == 4 ⋅ 7 ⋅ 7 − 2 21 + 7 + 2 21 = 7 ⋅ 2 + 7 = 21;е)( 12 + 2 18 ) ⋅2 − 96 = 12 ⋅ 2 + 2 18 ⋅ 2 − 96 == 4 ⋅ 3 ⋅ 2 + 2 9 ⋅ 2 ⋅ 2 − 2 24 ⋅ 3 ⋅ 2 = 2 6 + 12 − 4 6 = 12 − 2 6 .№421()3 12 − 2 27 = 3 ⋅ 4 ⋅ 3 − 2 3 ⋅ 9 ⋅ 3 = 3 ⋅ 2 − 2 ⋅ 3 ⋅ 3 = 6 − 18 = −12;а)()б) 5 2 − 7 3 ⋅ 6 = 5 2 ⋅ 6 − 7 3 ⋅ 6 == 5 ⋅ 2 3 − 7 ⋅ 3 2 = 10 3 − 21 2;8−в)( 10 − 5 ) ⋅5 = 8 − 5⋅5⋅2 + 5 ⋅ 5 == 2 ⋅ 4 − 5 2 + 5 = 2 2 − 5 2 + 5 = 5 − 3 2;()48 − 2 3 ⋅ 2 − 5 12 = 16 ⋅ 3 − 2 ⋅ 2 3 + 2 3 ⋅ 5 4 ⋅ 3 =г)= 4 3 − 4 3 + 10 ⋅ 3 ⋅ 2 = 60.№422а)(1 + 3 2 )(1 − 2 2 ) = 1 − 2 2 + 3 2 − 3 2 ⋅ 2 2 = 1 +б) (3 + 3 )(2 + 3 ) = 3 ⋅ 2 + 3 3 + 2 3 + 3 ⋅ 3 == 6 + 5 3 + 3 = 9 + 5 3;()(2 − 6 ⋅ 2 = 2 − 11;)в) 2 2 − 3 3 2 − 2 3 == 2 2 ⋅3 2 − 2 2 ⋅2 3 − 3 3 ⋅ 2 + 2 3 ⋅ 3 == 6 ⋅ 2 − 4 6 − 3 6 + 2 ⋅ 3 = 18 − 7 6 ;г)(5− 8)()5 − 3 2 = 5 ⋅ 5 − 5 ⋅3 2 − 8 ⋅ 5 + 3 2 ⋅ 8 == 5 − 3 10 − 4 ⋅ 2 ⋅ 5 + 3 2 ⋅ 4 ⋅ 2 == 5 − 3 10 − 2 10 + 3 ⋅ 2 ⋅ 2 = 17 − 5 10 ;(д) 2 5 + 12)( 12 − 5 ) −135 == 2 5 ⋅ 12 − 2 5 ⋅ 5 + 12 ⋅ 12 − 5 ⋅ 12 − 135 == 2 ⋅ 2 15 − 10 + 12 − 2 15 − 9 ⋅ 3 ⋅ 5 == 4 15 + 2 − 2 15 − 3 15 = 2 − 15;(е) 3 2 − 27)( 27 − 2 )−54 == 3 2 ⋅ 27 − 3 2 ⋅ 2 − 27 ⋅ 27 + 2 ⋅ 27 − 54 == 3 ⋅ 3 6 − 6 − 27 + 2 ⋅ 9 ⋅ 3 − 9 ⋅ 3 ⋅ 2 == 9 6 − 33 + 3 6 − 3 6 = 9 6 − 33№423а) x + y x − y = x 2 − y ;( )( )б) ( a − b )( a + b ) = a ⋅ a − b ⋅ b = a − b ;в) ( 11 − 3)( 11 + 3) = 11 ⋅ 11 − 3 ⋅ 3 = 2 ;( 10 + 7 )( 7 − 10 ) = 7 ⋅ 7 − 10 ⋅ 10 = 7 − 10 = −3 ;д) ( a + b ) = ( a ) + 2 a ⋅ b + ( b ) =222= a+2 a ⋅ b +b;е)( m − n) = ( m) −222m⋅ n+( n) =2= m−2 m ⋅ n +n ;( 2 + 3) = ( 2 ) + 2 2 ⋅ 3 + 3 = 11 + 6з) ( 5 − 2 ) = ( 5 ) − 2 5 ⋅ 2 + ( 2 ) =2ж)22222;2= 7 − 2 10 .№424а) 2 5 + 1 2 5 − 1 = 4 5 ⋅ 5 − 1 = 4 ⋅ 5 − 1 = 19 ;(б) (5)()()) ( )27 − 13 13 + 5 7 = 5 7 − 13 ⋅ 13 == 25 ⋅ 7 − 13 = 175 − 13 = 162 ;()() ( ) ( )г) (0,5 14 + 3 )( 3 − 0,5 14 ) = ( 3 ) − (0,5 14 ) =22в) 3 2 − 2к3 2 3 + 3 2 = 3 2 − 2 3 = 9 ⋅ 2 − 4 ⋅ 3 = 18 − 12 = 6 ;22= 3 − 0,25 ⋅ 14 = 3 − 3,5 = −0,5 ;()( )22д) 1 + 3 5 = 1 + 2 ⋅ 1 ⋅ 3 5 + 3 5 = 1 + 6 5 + 9 ⋅ 5 == 46 + 6 5 ;() ( )22е) 2 3 − 7 = 2 3 − 2 ⋅ 7 ⋅ 2 3 + 7 2 == 12 + 49 − 28 3 = 61 − 28 3 ;() ()22ж) 2 10 − 2 = 2 10 − 2 ⋅ 2 10 ⋅ 2 += 40 − 4 ⋅ 2 5 + 2 = 42 − 8 5 ;() ( )2( 2) =2( )22з) 3 6 − 2 3 = 3 6 − 2 ⋅ 3 6 ⋅ 2 3 + 2 3 == 9 ⋅ 6 − 12 2 ⋅ 3 ⋅ 3 + 4 ⋅ 3 = 66 − 36 2 .№425а)( 6 + 5) −2120 =( 6) + 226⋅ 5+( 5) −2= 6 + 2 30 + 5 − 4 ⋅ 3 ⋅ 2 ⋅ 5 = 11 ;60 +б)( 3 − 5) =215 ⋅ 4 +( 3) − 223⋅ 5 +12 ⋅ 10 =( 5) =2= 2 15 + 3 − 2 15 + 5 = 8 ;( 14 − 3 2 ) + 6 28 == ( 14 ) − 2 ⋅ 14 ⋅ 3 2 + (3 2 ) + 62в)224⋅7 == 14 − 3 ⋅ 2 4 ⋅ 7 + 9 ⋅ 2 + 6 ⋅ 2 7 = 14 + 18 = 32 ;()= (3 5 ) + 2 ⋅ 3 5 ⋅2г) 3 5 + 15 − 10 27 =2( )215 + 15 − 10 9 ⋅ 3 == 9 ⋅ 5 + 6 5 ⋅ 3 ⋅ 5 + 15 − 10 ⋅ 3 3 = 60 + 30 3 − 30 3 = 60 ;2д)  4 + 7 + 4 − 7  =22=  4 + 7  + 2 4 + 7 ⋅ 4 − 7 +  4 − 7  == 4 + 7 + 2 4 + 7  4 − 7  + 4 − 7 =()= 8 + 2 42 − 7 2  = 8 + 2 16 − 7 = 8 + 2 9 == 8 + 6 = 14;2е)  5 + 2 6 − 5 − 2 6  =22=  5 + 2 6  − 2 5 + 2 6 ⋅ 5 − 2 6 +  5 − 2 6  == 5 + 2 6 − 2 5 + 2 6  ⋅  5 − 2 6  + 5 − 2 6 = ()= 10 − 2 25 − 4 ⋅ 6 = 10 − 2 1 = 8 .№426( x + 1)( x − 1) = ( x ) − 1 = x − 1;б) ( x − a )( x + a ) = ( x ) − ( a ) = x − a;в) ( m + 2 ) = ( m ) + 2 m ⋅ 2 + ( 2 ) = m + 2 2m + 2;г) ( 3 − x ) = ( 3 ) − 2 3 ⋅ x + ( x ) = 3 − 2 3x + x;д) (5 7 − 13)(5 7 + 13) = (5 7 ) − 13 = 175 − 169 = 6;е) (2 2 + 3 3 )(2 2 − 3 3 ) = (2 2 ) − (3 3 ) = 4 ⋅ 2 − 9 ⋅ 3 = −19;ж) (6 − 2 ) + 3 32 = 6 − 2 ⋅ 6 2 + ( 2 ) + 3 16 ⋅ 2 =2а)2222222222222222= 36 − 12 2 + 2 + 3 ⋅ 4 2 = 38;з)( 2 + 18 ) − 30 = ( 2 ) + 222( )22 ⋅ 18 + 18 − 30 == 2 + 2 2 ⋅ 2 ⋅ 9 + 18 − 30 = 20 + 12 − 30 = 2 .№427а) x 2 − 7 = x − 7 x + 7 ;()()( 5 − c )( 5 + c);в) 4a − 3 = (2a − 3 )(2a + 3 ) ;г) 11 − 16b = ( 11 − 4b )( 11 + 4b ) ;д) y − 3 = ( y − 3 )( y + 3 );е) x − y = ( x − y )( x + y ) .б) 5 − c 2 =22№428а) 3 + 3 = 3 ⋅ 3 + 3 = 3 3 + 1 ;()б) 10 − 2 10 = 10 ⋅ 10 − 2 10 = 10 ( 10 − 2) ;в) x + x = x + x ⋅ x = x (1 + x ) ;г) a − 5 a = a ⋅ a − 5 a = a ( a − 5) ;()m ( 3 + 5 );д)a − 2a = a − 2 ⋅ a = a 1 − 2 ;е)3m + 5m = 3 ⋅ m + 5 ⋅ m =()ж) 14 − 7 = 7 2 − 1 ;з)№429а)б)в)г)д)е)ж)з)и)b2 − 5m+ 66−m(b − 5 )(b + 5 ) = b +=b− 5б))m+ 6( 6 − m)( 6 + m)=22− x=x−42− xb +3=b+ a6 −m1=−x +2;;b −3;b +3a −b1=( x − 2)( x + 2)( b − 3)( b + 3) ==b−95;b− 5( a − b )( a + b ) =a+ ba− b;2 x −3 y2 x −3 y1==;4x − 9 y2 x −3 y 2 x +3 y2 x +3 y7 −7a− a3+ x3 x+xx+ 25 −a5 − a27 −1a=a −1x2 − 2()()7 (1 − 7 )7 ( 7 − 1)=−=−=7 −17 −1( a − 1) =a −1=№430а)(33 + 22 = 3 ⋅ 11 + 2 ⋅ 11 = 11 3 + 2 .==3+ x(x 3+ x)=a;1x.(x − 2 )(x + 2 ) = x −2;x+ 25 −a( 5 − a )( 5 + a ) =15 +a;7;в)г)д)е)ж)з)и)1x −5x −5;==−25 − x5− x 5+ x5+ x(2 +2)(2+ 2⋅ 2=25 + 1022 3 −35⋅ 22 3− 3⋅ 3=5 3x+ xa+ aa a +ax=( x + 1)=1a⋅ a+ a()=x 5;5=3 b;ba a +12(( a − b)=3( a − b )x +1=) = 1+5+ 2=5 32=3 a −3 b23 2− 3=5 32a − 2bx +1(2 1+ 2=5⋅ 5+ 5⋅ 2=10)б)в)г)д)е)xx 5=53b7 yb b3 b=2a5⋅ 5b⋅ b==4a+b1a −b2 y7 y⋅ ya bb b⋅ b==(==52;3;x=a(( a + 1) =)a a +12 y;7ya b a b= 2 ;b ⋅bb4 a+b)( a + b )( a + b )1⋅ a − b( a − b )( a − b );)= 2−№431а)2;()=4 a+b;a+b=a −b;a −ba.a3;ж)з)и)5=2 38=3 23 55 32 3⋅ 38 23 2⋅ 23 5⋅ 2=5 25 2⋅ 2=5 3 5 3;=2⋅36=8 2 4 2;=3⋅ 23=3 10 3 10== 0,3 10 .5⋅210№432а)б)в)г)д)е)mm x=x1x⋅ x1⋅ 2=23=5 ca2 32⋅ 2=32 354 15=m x;x=2;23⋅ c5 c⋅ ca 32 3⋅ 3=3 32 3⋅ 3==3 c;5c=a 3;6=3 33;=2⋅325 154 15 ⋅ 15=5 1515.=4 ⋅ 1512433.а)б)в)г)д)4( 3 − 1)4( 3 − 1)4( 3 − 1)4 == 2( 3 − 1);==223 −13 + 1 ( 3 + 1)( 3 − 1) ( 3 ) − 11 = 1 ⋅ (1 + 2 )= 1 + 2 = 1 + 2 = − 1 + 2 = −(1 + 2 );1− 211 − 2 (1 − 2 )(1 + 2 ) 1 − ( 2 ) 21x− yaa+ b337−3 3===1⋅ ( x +y)( x − y )( x +y)a( a − b )( a + b )( a − b )33(7 + 3 3 )(7 − 3 3 )(7 + 3 3 )===x+ y( x )2 − ( y )2a( a − b )( a )2 − ( b )233(7 + 3 3 )7 2 − 32 ⋅ ( 3 ) 2===x+ y;x− ya( a − b );a−b33(7 + 3 3 )=22=е)3(7 + 3 3 );2152 5 +5=−15(2 5 − 5)=15(2 5 − 5)=(2 5 + 5)(2 5 − 5)2(2 5 ) − 5=215(2 5 − 5)=4 ⋅ 5 − 2515(2 5 − 5)= −3(2 5 − 5) = 15 − 6 5 .5435.а)б)xx+b(x +y )( x − y )b( a + b )=a− b( a − b )(a + b )4в)=x( x − y )=y=10 − 2x( x − y )==x2 − ( y )2ab + b ba 2 − ( b )24( 10 + 2 )( 10 − 2 )( 10 + 2 )=x( x − y )==x2 − yab + b ba2 − b4( 10 + 2 )2( 10 ) − ( 2 )2;;=4( 10 + 2 )=8( 10 + 2 );212г)12( 3 − 6 )=3+ 6( 3 + 6 )( 3 − 6 )=12( 3 − 6 )2( 3) − ( 6 )2=−12( 3 − 6 )=3= 4( 6 − 3 );д)93−2 29(3 + 2 2 )=(3 − 2 2 )(3 + 2 2 )=9(3 + 2 2 )32 − ( 2 2 ) 2=9(3 + 2 2 )=9 − 4⋅2= 9(3 + 2 2 );е)=14=1+ 5 214 (1 − 5 2 )(1 + 5 2 )(1 − 5 2 )=14 (1 − 5 2 )12 − ( 5 2 ) 2=14(1 − 5 2 )2 ⋅ 7(1 − 5 2 ) 2(5 2 − 1).=−=1 − 507⋅77436.а)3=535б)2=aa2==3⋅ 55⋅ 52⋅ aa⋅ a=15= 0,2 15 , что и требовалось доказать;5=2a 1=2a , что и требовалось доказать.aa437.а)x=3x⋅ 3б)5=a5⋅ aв)2=32⋅ 3г)11⋅ 22;==222⋅ 2д)a2=23⋅ 3a⋅ a3⋅ 33x;3=5a;a6;3=a2 ⋅ 22⋅ 22=a 2; а≥044x 2 − x 2=4x2 −x=4а)m=9mб)a=7a⋅ 7в)cc==1212г)8=aе)=3x 24=x 3; x≥02438.9=7⋅ 74⋅ 2am;3=7a;7c3⋅ 4==c⋅ 33⋅ 4 ⋅ 34⋅ 2⋅ aa⋅ a==3c;62 2a.aУПРАЖНЕНИЯ ДЛЯ ПОВТОРЕНИЯ439.9 − x28x(3 − x )(3 + x) ⋅ 8 x(3 − x )( x + 3) ⋅ 8 x⋅ 2−2=−2=−2=24x4 x( x + 3)4 x ( x + 3) 2x + 6x + 9=2(3 − x) − 2( x + 3) 6 − 2 x − 2 x − 64x2(3 − x );−2===−x+3x+3x+3x=3подставляем x=-2,5 и находим:−4x−4 ⋅ (−2,5) 10=== 20.0,5x+3− 2,5 + 3440.Обозначим за S км – расстояние от А до В, тогда времявелосипедиста в пути равноSSч;ч – время мотоциклиста в1248пути.

Характеристики

Список файлов книги