mordkovitch-gdz-8-2002 (542435), страница 15
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а)4356 = 66; б)625. а)600 ,6 =≈ 0,77 ; б)10в)6000 = 60 ⋅10 ≈ 77 ;626. а)в)8464 = 92; в)г)3844 = 62; г)240 = 4 ⋅ 60 ≈ 15, 4 ;540 = 9 ⋅ 60 ≈ 23,1 .810 = 9 ⋅ 90 ≈ 28,5 ;2250 = 25 ⋅ 90 ≈ 47,5;б)360 + 2 = 4 ⋅ 90 + 2 ≈ 21;г)9000 − 4 = 90 ⋅10 − 4 ≈ 91 .xy = x ⋅ y ; б) x < 0; y < 0,627. a) x > 0; y > 0,9025 = 95.xy = − x ⋅ − y .628. а) а + b = a + b ; верно при а = 0 b = 0; a = 1 и b = 0;не верно при а = 2 b = 1; a = 2 и b = 2;б) ab = a b ; верно при а = 0, b = 1; a = 1 и b = 1;не верно при а = 2 b = 1; a = 2 и b = 2;в) а − b = a − b ; верно при а = 1, b = 0; a = 0 и b = 0;не верно при а = 2 b = 1; a = 3 и b = 1;г) ab = ab ; верно при а = 0 ; b = 2 ; a = 1 и b = 1;не верно при a = 2 , b = 3 ; a = 3 и b = 4.629.
а) f (4x) = − 4 х = −2 х = 2 f (x); б) f (x4) = − х 4 = – х2 = – (f (x))4;х = 0,1 f (x); г) f (x5) = − х5 = – х2 ·в) f (0,01x) = – 0,1х = х2 · f (x).§ 20. Преобразование выражений, содержащих операциюизвлечения квадратного корня.630. а)в)212 = 26 = 64 ;631. а)в)54 = 52 = 25;( −2 )8г)( −5 )2 = 52 = 5 .34 ⋅ 52 = 32 ⋅ 5 = 45 ; б)72 ⋅ 26 = 7 ⋅ 23 = 56 ;в) При b = 2, – 3633.г)= ( −2 )4 = 16 ;26 ⋅ 74 = 23 ⋅ 72 = 392 ;34 ⋅ 52 = 32 ⋅ 5 = 45 .а 2 = а = 15.
б) При а = 7, 2 а 4 = 2а2 = 98.632. а) При а = 15,а)б)b6 = – 3b3 = – 24. г) При y = – 2, 5 y8 = 5y4 = 80.9а16 = 9 ⋅ а16 = 3a8 ; б)36b8 = 6 b4 ; в)49c 4 = 7 с2 ; г)81d 6 = 9 d3 .634. а) – 5 4 х2 = – 5 · 2x = – 10x; б) –3 9 у 6 = – 3 · 3у3 = – 9у3;в) – 0,1 100 z8 = – 0,1 · 10z4 = – z4; г) – 0,25t 2 = – 0,5t.635.a)х 2 у 4 = х ⋅ у 2 ; б)636. а)z 6t 8 = z 3 ⋅ t 4 ; в)25а 4b6 = 5a 2b3 ;m12 n16 = m6 ⋅ n8 ; г)б)p8q10 = p 4 ⋅ q5 .81 12 269p q = p 6 q13 ;497141www.gdz.pochta.ruв)36m2 n8 = 6m ⋅ n4 ;1 18 21r s = r9s .24г)637.а)4a 2 2a= 3 ; б)b6b169a18 13a9; в)=256b30 5b15638.
а) 12 = 2 3 ; б)639. а)20 = 2 5 ; в)275 = 25 ⋅11 = 5 11 ;675 = 225 ⋅ 3 = 15 3 ;2245 = ⋅ 3 5 = 2 5 ;640. а)331в)200 = 2 ;10в)641. а)82 2=; б)27 3 3642. а) 1в) 149a18 7a9= 3 ; г)81b69b32 = 4 2 ; г) 54 = 3 6 .363 = 3 ⋅121 = 11 3 ;б)г) 108 = 3 ⋅ 36 = 6 3 .11120 = ⋅ 2 30 = 30 ;2211150 = ⋅ 5 6 = 6 .г)55б)40 2 10=; в)63 3 7113 1 13==;1212 2 31345 3 5;==3232 4 2576а12 24a6= 13 .25b265b54 3 6=; г)125 5 518б) 10 =г) 1243 9 3=.128 8 2108 6 33==3;822 21798 7==2;8181 9643. а) А= 3 50 V 2 98 = В; 450 V 392; 450 >392, т.е. А > В;б) А= 5 27 V 4 48 = В; 15 3 V 16 3 ; 15 3 < 16 3 , т.е.
А < В;в) А= 3 12 V75 = В; 180 V 75 108 >75, т.е. А > В;г) А= 10 8 V 5 32 = В; 10 8 V 10 8 ; 10 8 = 10 8 , т.е. А = В.8150550 = В; 8 VV; 8 > 5 ; т.е. А > В;93995151563 V 4,5 28 = В;7V9 7 ;7 < 9 7 , т.е. А < В;б) А=222644.
а) А= 3в) А= 381656550 = В;2 V2;2>2 , т.е. А > В;V7777749г) А= 0,5 108 V 3 3 = В; 3 3 V 3 3 ; 3 3 = 3 3 т.е. А = В.645. а)4а = 2 а ; б)25b = 5 b ; в)646. а)а3 = а а ; б)b5 = b2 b ; в)647. а)х15 у 2 = х7 у х ;в) m21n16 = m10 n8 m ;648.а) 100 х3 = 10 х х ;в)14296 у 5 = 4 у 2 6 у ;16c = 4 c ; г)49d = 7 d .c7 = с3 c ; г)d 11 = d 5 d .б)х8t 9 = х 4t 4 t ;г)р10 q13 = p5q 6 q .б)32 у 4 = 4 у 2 2 ;г)50t11 = 5t 5 2t .www.gdz.pochta.ru649.а)m3 m m=; б)n nn3650.
а)в)x3xx=; в)8 y3 2 y 2 y50m4 n3 5m2 n2n ;=9r 43r 272а 6b7 6a3b3 2b=;49 y 87 y481с6с3=93аа1; г)а32с7 4с3=2c .9b6 3b3б)3x y9 x2 y=;2z4z 2г)27 x11 y13 3x5 y 6 3 xy=.25ω 65ω3В ответе в пункте в) допущена ошибка.651. а) 2 3 = 12 ;б) 5 2 = 50 ;в) 11 5 = 121 ⋅ 5 = 605 ;г) 7 6 = 49 ⋅ 6 = 294 .652. а) −3 8 = − 72 ; б) −11 3 = − 363 ; в) −13 5 = − 845 ; г) −6 2 = − 72 .653.а)152416 ⋅ 358032 = 2 ; б) −8 = − 50 ; в) −9 = − 4 ; г).=35 =7497423654. а) х 12 = 12 х 2 ; б) у 32 = 32 у 2 ; в) z 5 = 5 z 2 ; г) t 11 = 11t 2 .655.а) а2 7 =74а 4 ; б) −b 10 = − 10b2 ; в) с21= − 3х 4 ;3656. а) −3х281 =81с 4 ; г) − d 3 = − 3d 2 .б) 4х2у 0,5 ху = 8 х5 у 3 ;в) −5m6 5m = − 125m13 ;г)120qp= 5 pq .2p657. а) 2 х + 3 х – 5 х =0; б) 6 у + 4 у – у = 9 у ;в) –3 z +z + 9 z = 7 z ; г)658.
а) 5 а + 3 b –б) 8 c +в)d –а +2 b =4q +n + 11 m = 10 m + 2 n ;р –q +5р =3659. а) 4 2 – 18 = 4 2 – 3 2 =б)а +5 b;d –4 c=4 c;m + n –2 m +г) – 3 р + 4t – 2 t + 15 t = 14 t .2;216 – 2 6 = 6 6 – 2 6 = 4 6 ; в)г) 125 + 7 5 = 5 5 + 7660. а)р +3 q .243 + 3 3 = 9 3 +3 3 =12 3 ;5 = 12 5 .20 + 125 = 2 5 + 5 5 = 7 5 ; б)18 − 8 = 3 2 − 2 2 = 2 ;в) 27 + 48 = 3 3 + 4 3 = 7 3 ; г) 32 − 128 = 4 2 − 8 2 = −4 2 .661.а) 5 3 – 300 – 27 = 5 3 – 10 3 – 3 3 = – 8 3 ;б) 3 5 +20 +80 = 3 5 + 2 5 + 4 5 =9 5 ;143www.gdz.pochta.ruв) 6 3 +27 –48 = 6 3 + 3 3 – 4 3 = 5 3 ;г) 5 2 +32 –200 = 5 2 + 4 2 – 10 2 = –2.662. а) 2 125 + 2 201 – 2 = 10 5 + 4 5 – 8 5 = 6 5 ;б) 3 12 + 2 3 – 2 27 = 6 3 + 2 3 – 6 3 = 2 3 ;в) 3 8 + 128 –800 = 6 2 + 8 2 – 20 2 = – 6 2 ;г) 5 12 – 2+ 2 27 = 10 3 – 8 3 + 6 3 = 8 3 .663.
а)32 +50 –98 = 4 2 + 5 2 – 7 2 = 2 2 ;б)147 +12 +75 = 7 3 + 2 3 + 5 3 = 14 3 ;в)50 +98 –200 = 5 2 + 7 2 – 10 2 = 2 2 ;г)20 + 2 45 – 3 500 = 2 5 + 6 5 – 30 5 = – 22 5 .664. а)9а +25а –36а = 3 а + 5 а – 6 а = 2 а ;б)5b – 2 20b – 3 80b =в)8c –50c +5b – 4 5b – 12 5b = – 15 5b ;18c = 2 2c – 5 2c + 3 2c = 0;г) 0,1 5m – 0, 45m +2 80m =0,1 5m –0,3 5m +8В задачнике в пункте г) опечатка.665.
а) 3 2 + 2 32 +12128 = 3 2 + 8 2 +5m =7,8 5m .2 = 15 2 ;127 + 48 = 5 3 + 3 + 4 3 = 10 3 ;32600 −54 − 6 = 10 6 − 2 6 − 6 = 7 6 ;3б) 5 3 +в)20 + 2 45 − 3 500 = 2 5 + 6 5 – 30 5 = – 22 5 ;1666. а) 2 8 + 0,5 32 − 18 + 50 = 4 2 + 2 2 − 2 + 5 2 = 10 2 ;3172 − 200 = 17 ,5 2 − 5 2 − 0,5 2 − 10 2 = 2 2 ;б) 2,5 98 − 2,5 8 −21в)75 + 3 48 − 147 + 300 + 27 = 3 + 12 3 − 7 3 + 10 3 + 3 3 = 19 3 ;5121г) 2 − 162 −27 +300 = 2 – 2 – 2 3 + 2 3 = 0.935г)667. а) 5 +12б) 3 2у –8у + 0,1 200 у = 3 2у – 2 2 у +12 х – 100,03х = 5 3х +3х –3х = 5 3х ;2 у = 2 2у ;в) 4 3t – 12t + 2 75t = 4 3t – 2 3t + 10 3t = 12 3t ;г) 5 27t – 4 48t – 2 12t = 15 3t – 16 3t + 4 3t = – 5 3t .668.
а)144a3b +22a5a5b = a a3b +ab = a ab ;3a33www.gdz.pochta.ruб) 2аa 7b + a9b = 2a 4 ab − a 4 ab = a 4 ab ;m 3 + 4 m m3 − m 2 m = m 2 m + 4 m 2 m − m 2 m = 4 m 2 m ;34d 5 = 9 d – 5d d + 6d d = 10d d .г) 81d 3 − 5d d +dв)669.а) 3 ⋅ 2 6 = 6 2 ; б)670.а) 5 3 : 5 = 3 ; б)5 ⋅ 2 15 = 10 3 ; в) 6 3 ⋅ 27 = 54 ; г) 3 2 ⋅ 8 = 12 .161172 : 2 = ; в) 6 5 : 3 = 2 5 ; г)30 : 5 =6.5533671. а) (3 12 − 75 ) ⋅ 3 = ( ( 6 3 − 5 3 ) ⋅ 3 ) = 3;б) (3 51 − 2 3 ) ⋅ 5 = 15 – 2 15 ;в) ( 12 + 2 18 ) ⋅ 2 = ( 2 3 + 6 2 ) ⋅ 2 = 2 6 + 12;г) 2 3( 2 − 5 12 ) = 4 3 – 60.672. а) ( 8 − 24 ) ⋅ 2 = (2 2 – 2 6 ) ⋅ 2 = 4 – 4 3 ;б) ( 3 – 27 ) ⋅ 3 = ( 3 – 3 3 ) ⋅ 3 = – 6; в) ( 2 – 22 ) ⋅ 2 = 2 – 2 11 ;г) ( 0, 27 + 75 ) ⋅ 48 = (3103 + 5 3 ) · 4 3 = 63,6.673. а) (5 2 – 18 ) ⋅ 2 = (5 2 – 3 2 ) ·2 = 4;б) (3 5 – 2 20 ) ⋅ 5 = 3 ( 5 – 4 5 ) ·5 = – 5;в) ( 50 – 2 2 ) ⋅ 5 = (5 2 – 2 2 ) ·2 = 6;г) (4 3 + 27 ) ⋅ 3 = (4 3 + 3 3 ) ·3 = 21.674.
а) ( 20 − 2 3 + 5 ) ⋅ 5 = (2 5 – 2 3 +б) (3 5 –5)5 = 15 – 2 15 ;6 + 1) · 2 2 = 6 10 – 4 3 + 2 2 ;в) (2 3 + 15 – 10 ) · 5 = 2 15 + 5 3 – 5 2 ;г) (4 3 – 2 6 – 1) · 2 3 = 24 – 12 2 – 2 3 .675. а)в)х ⋅ ( а − b ) = ax − bx ; б) ( c + d ) c = с+ cd ;mn ( m +n ) = m n + n m ; г) (676. а) ( 50 + 6 ) :2 =5+p– q)pq = p q – q3 ; б) ( 28 − 44 ) : 2 =7–p.11 ;в) ( 2 45 − 4 63 ) : 6 = (6 5 + 12 7 ) : 6= 5 + 2 7 ;г) ( 12 − 2 54 ) : 2 3 = (2 3 – 6 6 ) : 2 3 = 1 – 3 2 .677.а) (12 45 − 6 20 ) : 3 5 = (36 5 – 12 5 ) : 3 5 = 8;б) (4 7 − 2 12 ) : 2 3 = (20 3 + 4 3 ) : 2 3 = 12;в) (15 44 − 24 99 ) : 3 11 = (30 11 – 72 11 ) : 3 11 = – 14;г) ( 28 − 2 ⋅ 52 + 2 63 ) :7 = (2 7 – 6 7 + 6 7 ) :7 = 2.145www.gdz.pochta.ru678.
а) (2 +6 ) (3 2 – 2 3 ) == 6 2 +3 12 – 4 3 – 2 18 = 6 2 + 6 3 – 4 3 – 6 2 = 2 3 ;б) (1 + 15 ) ( 3 – 5 ) =в) (3 +3 –5+35–5 3=2 5 –4 3;21 ) ( 3 – 7 ) = 3 + 3 7 – 3 7 – 7 = – 4 3 ;г) (2 5 –3 ) ( 3 + 3 5 ) = 2 15 – 3 + 30 – 3 15 = – 15 + 27.679. а) (2 5 – 3 2 + 1) ( 5 – 2 ) = 10 – 3 10 += 16 – 5 10 +5 –5 – 2 10 + 6 –2=2;б) ( 3 –2 2 + 5 ) ( 3 – 5 )=3–2 6 + 15 – 15 +2 10 –5=–2–2 6 +2 10 ;в) (2 6 –5 18 + 48 )( 2 – 3 )=4 3 –30+4 6 –6 2 +15 6 –12 == 19 6 + 4 3 – 6 2 – 42;г) ( 10 + 45 + 80 )(2 2 + 5 )=4 5 +6 10 +8 10 +5 2 +15+20== 35 + 4 5 + 14 10 + 5 2 .b ) (2а – 3 b ) = 2а2 + 2а b – 3b – 3a b = 2a 2 − a b − 3b ;680. а) (а +б) ( 12а – 75b ) (2 а +3b ) = 4а 3 – 10 3аb + 6 аb – 15b;в) ( m –2 n ) ( m – n )=m–2 mn – mn + 2n = m – 3 mn + 2n;г) ( а3 −b3 ) (2 а +b ) = 2а2 –2b аb + a аb – b2.681.
а) ( 7 – 5 )( 7 + 5 ) = 7 – 5 = 2; б) (а +в) ( 6 + 2 )( 6 –2 ) = 6 – 2 = 4; г)(b ) (а –3 р − 5q)(b ) = а2 –b;3 р + 5q)= 3p – 5q.682. а) ( 2 + 4)2=2+8 2 +16=18+8 2 ; б) ( 5 –1)2=5–2 5 +1=6–2 5 ;в) (2+ 17 )2=4+4 17 +17=21+4 17 ; г) (3– 8 )2=9–6 8 + 8 = 17 – 6 8 .683. а) (2 3 – 3 2 )2 = 12 – 12 6 + 18 = 30 – 12 6 ;б) ( 6 + 12 )2 = 6 + 12 12 + 12 = 18 + 12 2 ;в) (3 5 – 5 3 )2 = 45 – 30 15 + 75 = 120 – 30 15 ;г) ( 14 +22 )2 = 14 + 2 · 277 + 22 = 36 + 4 77 .2684. а) ( а + b ) = а + 2 аb + b; б) ( х – 3 у )2 = x – 6 ху + 9y;в) ( t + 2v )2 = t + 4tv + 4v; г) (2 m – 5 n )2 = 4m – 20 mn + 25n.2685.
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