makarytchev-gdz-7-1-1289-2003 (542427), страница 11
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а) 3ab(a2 – 2ab + b2) = 3a3b – 6a2b2 + 3ab2;б) –x2y(x2y2 – x2 – y2) = –x4y3 + x4y + x2y3;в) 2,5a2b(4a2 – 2ab + 0,2b2) = 10a4b – 5a3b2 + 0,5a2b3;г) (–2ax2 + 3ax – a2)(–a2x2) = 2a2x4 – 3a3x3 + a4x2;д) (6,3x3y – 3y2 – 0,7x) ⋅ 10x2y2 = 63x5y3 – 30x2y4 – 7x3y2;е) –1,4p2q6 (5p3q – 1,5pq2 – 2q2) = –7p5q7 + 2,1p3q8 + 2,8p2q9.№665.2x ⋅ (1,4x2 – 3,5y) = 0,4x3 – xy;71б) – c2 ⋅ (1,2d2 – 6c) = –0,4c2d2 + 2c3;334 ⎞ 1321⎛2в) ab ⎜ a 2 − ab + b2 ⎟ = a3b − a 2b2 + ab3 ;3453852⎝⎠2 2 5⎛1 25 ⎞112г) − a y ⎜ 5ay − a y − a3 ⎟ = −2a3 y 7 + a 4 y 6 + a5 y 5 .526 ⎠53⎝а)№666.а) –3x2(–x3 + x – 5) = 3x5 – 3x3 + 15x2;б) (1 + 2a – a2) ⋅ 5a = 5a + 10a2 – 5a3;в)2 2x y(15x – 0,9y + 6) = 10x3y – 0,6x2y2 + 4x2y;3г) –3a4x(a2 – 2ax + x3 – 1) = –3a6x + 6a5x2 – 3a4x4 + 3a4x;д) (x2y – xy + xy2 + y3) ⋅ 3xy2 = 3x3y3 – 3x2y3 + 3x2y4 + 3xy5;3 4a (2,1b2 – 0,7a + 35) = –0,9a4b2 + 0,3a5 – 0,9a4.7№667.
а) 3(2x – 1) + 5(3 – x) = 6x – 3 + 15 – 5x = x + 12,при x = –1,5, x + 12 = –1,5 + 12 = 10,5;б) 25a – 4(3a – 1) + 7(5 – 2a) = 25a – 12a + 4 + 35 – 14a = 39 – a,при a = 11, 39 – a = 39 – 11 = 28.в) 4 y − 2(10 y − 1) + (8 y − 2) = 4 y − 20 y + 2 + 8 y − 2 = −8 yпри y = −0,1,− 8 y = −8 ⋅ ( − 0,1) = 0 ,8 ;г) 12(2 − 3 p ) + 35 p − 9(p + 1) = 24 − 36 p + 35 p − 9 p − 9 = −10 p + 15при p = 2 , − 10 p + 15 = −10 ⋅ 2 + 15 = −5 .е) –76№668. а) 14b + 1 – 6(2 – 11b) = 14b + 1 – 12 + 66b = 80b – 11;б) 25(2 – 3c) + 16(5c – 1) = 50 – 75c + 80c – 16 = 5c + 34;в) 14(7x – 1) – 7(14x + 1) = 98x – 14 – 98x – 7 = –21;г) 36(2 – y) – 6(5 – 2y) = 72 – 36y – 30 + 12y = 42 – 24y.№669. а) 14y + 2y(6 – y) = 14y + 12y –2y2 = 26y – 2y2;б) 3y2 – 2y(5 + 2y) = 3y2 – 10y – 4y2 = –y2 – 10y;в) 4x(x – 1) – 2(2x2 – 1) = 4x2 – 4x – 4x2 + 2 = –4x + 2;г) 5a(a2 – 3a) – 3a(a2 – 5a) = 5a3 – 15a2 – 3a3 + 15a2 = 2a3;д) 7b(4c – b) +4c(c – 7b) = 28bc – 7b2 + 4c2 – 28bc = 4c2 – 7b2;е) –2y(x3 – 2y) – (x3y + 4y2) = –2x3y + 4y2 – x3y – 4y2 = –3x3y;ж) 3m2(m + 5n) – 2n(8m2 – n) = 3m2 + 15m2n – 16m2n + 2n2 = 3m3 – m2n + 2n2;з) 6m2n3 – n2(6m2n + n – 1) = 6m2n3 – 6m2n3 – n3 + n2.№670.
а) 6x(x – 3) – x(2 – x) = 6x2 – 18x – 2x + x2 = 7x2 – 20x;б) –a2(3a – 5) + 4a(a2 – a) = –3a3 + 5a2 + 4a3 – 4a2 = a3 + a2;в) ax(2x – 3a) – x(ax + 5a2) = 2ax2 – 3a2x – ax2 – 5a2x = ax2 – 8a2x;г) –4m2(n2 – m2) + 3n2(m2 – n2) == –4m2n2 + 4m4 + 3m2n2 – 3n4 = 4m4 – m2n2 – 3n4.№671.а) –2x(x2 – x + 3) + x(2x2 + x – 5) = –2x3+2x2 – 6x + 2x3 + x2 – 5x = 3x2 – 11x,при x = 3, 3x2 – 11x = 3 ⋅ 32 – 11 ⋅ 3 = 27 – 33 = –6,при x = –3, 3x2 – 11x = 3 ⋅ (–3)2 – 11 ⋅ (–3) = 27 + 33 = 60;б) x(x – y) – y(y2 – x) = x2 – xy – y2 + xy = x2 – y2,при x = 4; y = 2, x2 – y2 = 42 – 22 = 16 – 8 = 8.№672. а) 5x(2x – 6) – 2,5x(4x – 2) = 10x2 – 30x – 10x2 + 5x = –25x,при x = –8, –25x = –25 ⋅ (–8) = 200, при x = 10, –25x = –25 ⋅ 10 = –250;б) 5a(a – 4b) – 4b(b – 5a) = 5a2 – 20ab – 4b2 + 20ab = 5a2 – 4b2,при a = –0,6; b = –0,5, 5a2 – 4b2 = 5 ⋅ (–0,6)2 – 4 ⋅ (–0,5)2 = 1,8 – 1 = 0,8.№673.
а) (3a2)2 – a3(1 – 5a) = 9a4 – a3 + 5a4 = 14a4 – a3;31 ⎞11⎛ 1 ⎞⎛б) ⎜ − b ⎟ − b ⎜1 − 2b − b2 ⎟ = − b3 − b + 2b2 + b3 = 2b2 − b ;8 ⎠88⎝ 2 ⎠⎝в) x(16x – 2x3) – (2x2)2 = 16x2 – 2x4 – 4x4 = 16x2 – 6x4;г) (0,2c3)2 – 0,01c4(4c2 – 100) = 0,04c6 – 0,04c6 + c4 = c4.№674.EBCaAcbFDa ⋅ (b + c) = ab + ac, a ⋅ (b + c) = SABCD — площадь прямоугольника ABCD.a ⋅ b = SABEF a ⋅ c = SEFDC — площади прямоугольников ABEF и EFDC.Площадь ABCD равна сумме площадей ABEF и EFDC: SABCD = SABEF + SEFDC.77№675.
x(2x + 1) – x2(x + 2) + (x3 – x + 3) = 2x2 + x – x3 – 2x2 + x3 – x + 3 = 3.№676. y(3y2 – y + 5) – (2y3 + 3y – 16) – y(y2 – y + 2) == 3y3 – y2 + 5y – 2y3 – 3y + 16 – y3 + y2 – 2y = 16 не зависит от y.№677.а) a(b – c) + b(c – a) + c(a – b) = ab – ac + bc – ab + ac – bc = 0;б) a(b+c–bc)–b(c+a–ac) + c(b – a) = ab + ac – abc – bc + abc + bc – ac = 0.№678.2x(x – 6) – 3(x2 – 4x + 1) = 2x2 – 12x – 3x2 + 12x – 3 = –x2 – 3 т.к. –x2 ≤ 0;–3 < 0, а сумма неотрицательного и положительного чисел меньше нуля.№679.а) 5x + 3(x – 1) = 6x + 11, 5x + 3x – 3 – 6x = 11,2x – 3 = 11, 2x = 14, x = 7;б) 3x – 5(2 – x) = 54, 3x – 10 + 5x = 54, 8x = 64, x = 8;в) 8(y – 7) – 3(2y + 9) = 15, 8y – 56 – 6y – 27 = 15,2y – 83 = 15, 2y = 98, y = 49;г) 0,6 – 0,5(y – 1) = y + 0,5, 0,6 – 0,5y + 0,5 = y + 0,5,–0,5y – y = 0,5 – 1,1, 1,5y = 0,6, y = 0,4;д) 6 + (2 – 4x) + 5 = 3(1 – 3x), 6 + 2 – 4x + 5 = 3 – 9x,–4x + 9x = 3 – 13, 5x = –10, x = –2;е) 0,5(2y–1)–(0,5–0,2y) + 1 =0, y – 0,5 – 0,5 + 0,2y + 1 = 0, 1,2y = 0, y = 0;ж) 0,15(x – 4) = 9,9 – 0,3(x – 1), 0,15x – 0,6 = 9,9 – 0,3x + 0,3,0,15x + 0,3x = 10,2 + 0,6, 0,45x = 10,8, x = 24;5з) 3(3x – 1) + 2 = 5(1 – 2x) – 1, 9x + 10x = 4 + 1, 19x = 5, x = .19№680.а) 3x(2x – 1) – 6x(7 + x) = 90, 6x2 – 3x – 42x – 6x2 = 90, 45x = –90, x = –2;б) 1,5x(3 + 2x) = 3x(x + 1) – 30, 4,5x + 3x2 = 3x2 + 3x – 30,4,5x – 3x = –30, 1,5x = –30, x = –20;в) 5x(12x– 7) – 4x(15x – 11) = 30 + 29x, 60x2 – 35x – 60x2 + 44x = 30 + 29x,9x – 29x = 30, 20x = –30, x = –1,5;г) 24x – 6x(13x – 9) = –13 – 13x(6x – 1),24x – 78x2 + 54x = –13 – 78x2 + 13x, 78x – 13x = –13, 65x = –13, x = –1.5№681.
а) 3(–2x + 1) – 2(x + 13) = 7x – 4(1 – x),–6x + 3 – 2x – 26 = 7x – 4 + 4x, –8x – 23 = 11x – 4, 19x = –19, x = –1;б) –4(5 –2a) + 3(a – 4) = 6(2 – a) – 5a, –20 + 8a + 3a – 12 = 12 – 6a – 5a,–32 + 11a + 11a = 12, 22a = 44, a = 2;в) 3y(4y – 1) – 2y(6y – 5) = 9y – 8(3 + y),12y2 – 3y – 12y2 + 10y = 9y – 24 – 8y, 7y – y = –24, 6y = –24, y = –4;г) 15x + 6x(2 – 3x) = 9x(5 – 2x) – 36, 15x + 12x – 18x2 = 45x – 18x2 – 36,27x – 45x = –36, 18x = 36, x = 2.№682.
а) 4(1 – c) – 2(3 – 5c) = 1, 4 – 4c – 6 + 10c = 1, 6c = 3, c =0,5;б) –3(2x + 1) –(8x + 5) = 20, –6x – 3 – 8x – 5 = 20,–14x = 20 + 8, 14x = –28, x = –2;в) 3(5x + 7) = 61 – 10x, 15x + 21 = 61 – 10x, 25x = 40, x = 1,6;г) 2(7 + y) = 8 – y, 14 + 2y = 8 – y, 3y = –6, y = –2.78№683.а)x x+ = 14 ,4 33x + 4x = 168, 7x = 168, x = 24;401a a, a = 13 ;− = 5 , 4a – a = 40, 3a = 40, a =332 841yв) = y –1, y = 4y – 4, 3y = 4, y = , y = 1 ;3432z157, 10z + 15 = 2z, 8z = –15, z = – , z = – 1 ;г) 2z + 3 =5882c 4 cд)−= 7 , 10c – 12c = 105, 2c = –105, c = –52,5;355x xе)+ + 4 = 0 , 5x + 3x + 36 = 0, 8x = –36, x = –4,5;9 34a5a, 16a + 36 = 15a, a = –36;ж)+1 =9125m m 181з)− = , 10m – 3m = 8, 7m = 8, m = , m = 1 ;12 8 3773n n 2+ = , 3n + 7n = 4, 10n = 4, n = 0,4.и)14 2 76x − 5 2x − 1№684.
а)=+ 2 , 3(6x – 5) = 7(2x – 1) + 42,7318x – 15 = 14x – 7 +42, 4x = 50, x = 12,5;5 − x 3x − 1б)+= 4 , 5(5x – x) +2(3x – 1) = 40,2525 – 5x + 6x – 2 = 40, x + 23 = 40, x = 17;5x − 7 x − 5в)−= 5 , 2(5x – 7) – 3(x – 5) = 120,12810x – 14 – 3x + 15 = 120, 7x = 119, x = 17;4 y − 11 13 − 7 yг)+= 2 , 4(4y – 11) + 3(13 – 7y) = 120,152016y – 44 + 39 – 21y = 120, 5y = –125, y = –25;5 − 6y y8д)+ = 0 , 8(5 – 6y) + 3y = 0, 40 – 48y + 3y = 0, 45y = 40, y = ;38912y 3 − 2yе) −= 0 , 5y – 4(3 – 2y) = 0, 5y – 12 + 8y = 0, 13y = 12, y = .13453x + 5 x + 1№685.
а)−= 1 , 3(3x + 5) – 5(x + 1) = 15, 9x + 15 – 5x – 5 = 15,534x = 5, x = 1,25;2 p −1 p +1б)+= p , 2p – 1 – 2(p + 1) = 6p, 2p – 1 – 2p – 2 – 6p = 0,63–3 – 6p = 0, 6p = –3, p = –0,5;б)796y −1 y 2y1, 6y – 1 – 3y = 10y, 7y = –1, y = – ;− =1553712 − x 2 − x xг)−= , 3(12–x)–4(2–x) = 2x, 36 – 3x – 8 + 4x = 2x, x = 28.436x−3 2− x№686.
а) 1 −=+ 4 , 6 – 3(x – 3) = 2(2 – x) + 24,236 – 3x + 9 = 4 – 2x + 24, 15 – 3x = 28 – 2x, –3x +2x = 28 – 15, x = –13;a + 13 2a 3 − a a−=+ , 3(a + 13) – 12a = 2(3 – a) + 15a,б)1051523a + 39 – 12a = 6 – 2a + 15a, 39 – 9a = 6 – 39,–9a – 13a = 6 – 39, 22a = 33, a = 1,5;2m + 1m 6−mв), 3(2m + 1) + 26 = 2m – 6 + m,+3= −46126m – 3m = – 6 – 39, 3m = –45, m = –15;x +1 x −1x+3, 2(x + 1) – 3(x – 1) = 36 – 9x – 27,г)−= 2−9625 – x = 9 – 9x, 8x = 4, x = 0,5.6y + 7 8 − 5y№687. а)+= 5 , 3(6y + 7) + 4(8 – 5y) = 60,4318y + 21 + 32 – 20y = 60, –2y + 53 = 60, 2y = –7, y = –3,5;5a − 1 2a − 3=− 1 , 5(5a – 1) = 3(2a – 3) – 15,б)3525a – 5 = 6a – 9 – 15, 25a – 6a = 5 – 24, 19a = –19, a = –1;11x − 4 x − 9в)−= 5 , 2(11x – 4) – 7(x – 9) = 70,7222x – 8 – 7x + 63 = 70, 15x = 70 – 63 + 8, 15x = 15, x = 1;2c − 1 c c + 3, 4(2c – 1) + 9c = 6(c + 3),г)+ =9468c – 4 + 9c = 6c + 18, 17c – 6c = 18 + 4, 11c = 22, c = 2;3p −1 2 p + 6д)−− 1 = 0 , 3(3p – 1) – 2(2p + 6) – 72 = 0,24369p – 3 – 4p – 12 – 72 = 0, 9p – 4p = 72 + 12 + 3, 5p = 87, p = 17,4;1 − 2 x 3x + 20 xе) 5 −=+ , 60 – 3(1 – 2x) = 2(3x + 20) + 4x,46360 – 3 + 6x = 6x + 40 + 4x, 57 – 40 = 4x, 4x = 17, x = 4,25.№688.ЦенаКол-воСтоимостьВсегооткрыткиx – 1/2 р1515(x – 1/2)36 рконвертыxр1010xблокноты4x р14xв)15(x –1) + 10x + 4x = 36, 29x = 43,5, x = 1,5 (р) стоит конверт.2Ответ: 1р; 1,5р; 6р.80№689.a2x + 4bxc2xP44 см2x + 4 + x + 2x = 44, 5x = 40,x = 8 см — одна сторона; 16 см — вторая; 20 см — третья.Ответ: 8см, 16см, 20см.№690.Если x т продали в I день, то (x + 3) т продали во II день, а в III день5( x + x + 3) т.
По условию за три дня продали 98 т.955x + (x + 3) + ( x + x + 3) = 98, 2x + 3 + (2x + 3) = 98,9918x + 10x + 15 = 855, 28x = 840,x = 30 т овощей продали в I день; 33 т продали во II день;5(30 + 33) = 35 т продали в III день.9Ответ: 30т, 33т, 35т.№691.БылоI сарай3x тII сарайxтВзяли20 тДобавилиСтало(3x – 20) т20 т(x + 20) т5от I75(3x– 20) = x + 20, 5(3x + 20 ) = x + 20, 15x – 100 = 7x + 140, 8x = 240,7x = 30 т сена было в I сарае; 90 т было во II сарае.Ответ: 30т, 90т.№692.Деталей в часВремяПо плануx дет.8с примен.
нового резца(x + 4) дет.20 тНорма8x6(x + 4)8x = 6(x + 4), 8x = 6x + 24, 2x = 24,x = 12 деталей за 1 час должен обтачивать по норме,12 ⋅ 8 = 96 деталей должен обтачивать по норме в день.Ответ: 96 дет.№693.га в деньДнейS лугапо плану50 гаx50xработали60 гаx–160(x – 1)50x = 60(x – 1), 10x = 60,x = 6 дней работали по плану. Тогда 50 ⋅ 6 = 300 га — площадь луга.Ответ: 300 га.81№694.I попыткаII попыткаv250 м/мин300 м/минtx мин(x – 1) минS250x км300(x – 1) кмодинаковое250x = 300(x – 1), 50x = 300, x = 6 мин — время I попытки;тогда длина 250 ⋅ 6 = 1500 м.Ответ: 1500 м.№695.vtSот турбазы допривалаобратно дотурбазы4,5 км/чxч4,5x км4 км/чxч4x кмна1ч больше4x 1x–= , 9x – 8x = 9, x = 9 км — расстояние от турбазы до привала.4 4,5 4Ответ: 9 км.№696.велосипедистмотоциклистv12 км/ч16 км/чtxчxчS12x км16x кмна 20 км больше16x – 12x = 20,4x = 20,x = 5, т.е.
через 5 ч мотоциклист догонит велосипедиста.12 ⋅ 5 = 60 км, значит через 60 км от A произойдет обгон.Ответ: 60 км.№697.vtSГрузовая машина60 км/чxч60x кмЛегковая машина90 км/ч(x – 2) ч90(x – 2) кмодинаковое60x = 90(x – 2), 30x = 180, x= 6 — через 6 ч легковая догонит грузовую.6 ⋅ 60 = 360 км — на расстоянии 360 км от A произойдет обгон.Ответ: 360 км.№698.а) 5x + 29 = –3x – 11, 8x = –40, x = –5, тогда y = 5 ⋅ (–5) + 29, y = 4,искомая точка — (–5; 4).б) 1,2x = 1,8x + 9,3, 0,6x = –9,3, x = –15,5, тогда y = 1,2 ⋅ (–15,5),y = –18,6, искомая точка — (15,5; –18,6).№699.а) y = –28x — II, IV четверть; б) y = 0,05x – 2,5 — I, II, IV четверть;в) y = 0,05x — I, III четверть; г) y = 0,05x – 2,5 — I, III, IV четверть.82№700.а)yy = x24y=4x0точки: (–2; 4); (2; 4)б)yy = x2y = 2x0xточки: (0; 0); (2; 2)№701.211⎛1⎞а) ⎜ a5 y3 ⎟ ⋅ (–ay)3 = a10y6(–a3y3) = – a13y999⎝3⎠б) –0,1a4b7 ⋅ (–30a2b)2 = –0,1a4b7 ⋅ 900a4b2 = –90a8b927.
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