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y2 ≥ 0 и 2 > 0.№743.а) n(n – 1) – (n + 3)(n + 2) = n2 – n – (n2 +5n + 6) = n2 – n – n2 – 5n – 6 == –6n – 6 = –6(n + 1) кратно 6;б) n(n + 2) – (n – 7)(n – 5) = n2 + 2n – (n2 – 12n + 35) == n2 + 2n + n2 + 12n – 35 = 14n – 35 = 7(2n – 5) кратно 7.№744.а) (3x–1)(5x+4)–15x2 = 17, 15x2 + 12x – 5x – 4 – 15x2 = 17, 7x = 21, x = 3;б) (1 – 2x)(1 – 3x) = (6x – 1)x – 1, 1 – 3x – 2x + 6x2 = 6x2 – x – 1,1 – 5x + 6x2 – 6x2 + x = –1, 4x = 2, x = 0,5;в) 12 – x(x – 3) = (6 – x)(x + 2), 12 – x2 + 3x = 6x + 12 – x2 – 2x,–x2 + 3x – 6x + x2 + 2x = 12 – 12, x = 0;г) (x + 4)(x + 1) = x – (x – 2)(2 – x), x2 + 5x + 4 = x – 2x + x2 + 4 – 2x,5x + 3x = 0, 8x = 0, x = 0.№745.а) 5 + x2 = (x + 1)(x + 6), 5 + x2 = x2 + 7x + 6, 7x = – 1, x = –1;7б) 2x(x – 8) = (x + 1)(2x – 3), 2x2 – 16х = 2x2 – x – 3, 15x = 3, x = 0,2;в) (3x – 2)(x + 4) – 3(x + 5)(x – 1) = 0, 3x2 + 10x – 8 – 3x2 – 12x + 15 = 0,2x = 7, x = 3,5;г) x2 + x(6 – 2x) = (x – 1)(2 – x) – 2, x2 + 6x – 2x2 = –x2 + 3x – 2 – 2,6x – 3x = –4, 3x = –4, x = –41, x = –1 .33№746.а) n(n + 5) – (n – 3)(n + 2) = n2 + 5n – n2 + n + 6 = 6n + 6 == 6 ⋅ (n+1) кратно 6;б) (n – 1)(n + 1) – (n – 7)(n – 5) = n2 – 1 – (n2 – 12 + 35) == n2 – 1 – n2 + 12 – 35 = 12n – 36 = 12 ⋅ (n – 3) кратно 12.№747.Если I число — x, то II число —(x + 1), а III число — (x + 2)x2 + 65 = (x + 1)(x + 2), x2 + 65 = x2 + 3x + 2, 3x = 63,x = 21 — I число; II число — 22; III число — 23.Ответ: 21; 22; 23.№748.Если I число — x, то II число —(x + 2), а III число — (x + 4)(x + 2)(x + 4) – (x + 2) ⋅ x = 76, x2 + 6x + 8 – x2 – 2x = 76, 4x = 68,x = 17 — I число; II число — 19; III число — 21.Ответ: 17; 19; 21.№749.P = 70 см;P= 35 см.

Если ширина x см, то длина — (35 – x) см.2I прямоуг.II прямоуг.Длина(35 – x) см(35 – x) – 5смШиринаx см(x + 5)смПлощадьx(35 – x) см2(30 – x)(x + 5) см289(x + 5) ⋅ (30 – x) = x(35 – x) + 50, 30x + 150 – 5x – x2 = 35x – x2 + 50,10x = 100, x = 10,25 см — длина, 10 см — ширина первого прямоугольника.Ответ: 10 см, 25 см.№750.a смb смS см2квадратxxx2прямоуг.x+3x–2(x + 3)(x – 2)на 30 см2 больше(x + 3)(x – 2) – x2 = 30, x2 + x – 6 – x2 = 30, x= 36 см — сторона квадрата.Ответ: 36 см.№751.Дет.

в деньДнейВсего дет.по плану54 дет.X54x дет.работали60 дет.x–160(x – 1) дет.на 18 дет. больше60(x – 1) – 54x = 18, 60x – 60 – 54x = 18, 6x = 18 + 60, 6x = 78,x = 13 дней по плану, 12 дней работала на самом деле.Ответ: 12.№752.га в деньДнейВсегопо плану112 гаx112x гаодинаковоработали120 гаx–1120(x – 1) га112x = 120(x – 1), 112x = 120x – 120, 8x = 120,x = 15 дней должны были работать по плану,112 ⋅ 15 = 1680 га всего вспахали.Ответ: 1680 га.№753.x − 2 2 3x − 2а), 6(x – 2) = 20 – 5(3x – 2), 6x – 12 = 20 – 15x + 10,= −5366x + 15x = 42, 21x = 42, x = 2;2x − 5x +1, 3(2x – 5) – 12 = 4(x + 1), 6x – 15 – 12 = 4x + 4,б)−1 =436x – 4x = 4 + 27, 2x = 31, x = 15,5.№754.а) сумма квадратов чисел a и b; б) квадрат суммы чисел a и b;в) разность кубов чисел a и b;г) куб разности чисел a и b.29.

Разложение многочлена на множителиспособом группировки№755.а) x(b + c) + 3b + 3c = x(b + c) + 3(b + c) = (b + c)(x + 3);б) y(a – c) + 5a – 5c = y(a – c) + 5(a – c) = (a – c)(y + 5);в) p(c – d) + c –d = p(c – d) + 1(c – d) = (c – d)(p + 1);г) a(p – q) + q – p = a(p – q) – (p – q) = (p – q)(a – 1).90№756. а) mx + my + 6x + 6y = m(x + y) + 6(x + y) = (x + y)(m + 6);б) 9x + ay + 9y + ax = 9(x + y) + a(x + y) = (x + y)(9 + a);в) 7a – 7b + an – bn = 7(a – b) + n(a – b) = a – b)(7 + n);г) ax + ay – x – y = a(x + y) – (x + y) = (x + y)(a – 1);д) 1 – bx – x + b = (1 + b) – x(1 + b) = (1 + b)(1 – x);е) xy + 2y – 2x – 4 = y(x + 2) – 2(x + 2) = (x + 2)(y – 2).№757. а) ab – 8a – bx + 8x = a(b – 8) – x(b – 8) = (b – 8)(a – x);б) ax – b + bx – a = a(x – 1) + b(x – 1) = (x – 1)(a + b);в) ax – y + x – ay = x(a + 1) – y(1 + a) = (a + 1)(x – y);г) ax – 2bx + ay – 2by = x(a – 2b) + y(a – 2b) = (a – 2b)(x + y).№758.

а) x3 + x2 + x + 1 = x2(x + 1) + (x + 1) = (x + 1)(x2 + 1);б) y5 – y3 – y2 + 1 = y3(y2 – 1) – (y2 – 1) = (y2 – 1)(y3 – 1);в) a4 + 2a3 – a – 2 = a3(a + 2) – (a + 2) = (a + 2)(a3 – 1);г) b6 – 3b4 – 2b2 + 6 = b4(b2 – 3) – 2(b2 – 3) = (b2 – 3)(b4 – 2);д) a2 – ab – 8a + 8b = a(a – b) – 8(a – b) = (a – b)(a – 8);е) ab – 3b + b2 – 3a = a(b – 3) + b(b – 3) = (b – 3)(a + b);ж) 11x – xy + 11y – x2 = 11(x + y) – x(y + x) = (x + y)(11 – x);з) kn – mn – n2 + mk = n(k – n) + m(k – n) = (k – n)(m + n).№759.

а) mn – mk + xk – xn = m(n – k) – x(n – k) = (n – k)(m –x);б) x2 + 7x – ax – 7a = x(x – a) + 7(x – a) = (x – a)(x + 7);в) 3m – mk + 3k – k2 = m(3 – k) + k(3 – k) = (3 – k)(m + k);г) xk – xy – x2 + yk = x(k – x) + y(k – x) = (k – x)(x + y).№760.а) x2 + ax – a2y – axy = x(x + a) – ay(a + x) = (a + x)(x – ay);б) a2n + x2 – anx – ax = an(a – x) – x(a – x) = (a – x)(an – x);в) 5a3c + 10c2 – 6bc – 3abc2=5a2(ac + 2) – 3bc(2 + ac)= (ac + 2)(5a2 – 3bc);г) 21a + 8xy3 – 24y2 – 7axy = 7a(3 – xy) + 8y2(xy – 3) == 7a(3 – xy) – 8y2(3 – xy) = (3 – xy)(7a – 8y2).№761.

а) p2q2 + pq – q3 – p3 = q2(p2 – q) – p(p2–q) = (p2 – q)(q2– p);при p = 0,5; q = –0,5 (p2 – q)(q2– p),(0,25 + 0,5)(0,25 –0,5) = 0,75(–0,25) = –0,1875;б) 3x3 – 2y3 – 6x2y2 + xy = 3x2(x – 2y2) +y(x – 2y2) = (x – 2y2)(3x2 + y);21при x= ; y= (x–2y2)(3x2+y),231 ⎞⎛ 4 1 ⎞ ⎛ 2 1 ⎞⎛ 4 1 ⎞ 1 11 11⎛2.⎜ − 2 ⋅ ⎟⎜ 3 ⋅ + ⎟ = ⎜ − ⎟⎜ + ⎟ = ⋅ =4 ⎠⎝ 9 2 ⎠ ⎝ 3 2 ⎠⎝ 3 2 ⎠ 6 6 36⎝3№762.а) 2a + ac2 – a2c – 2c = a(2 – ac) – c(2 – ac) = (2 – ac)(a –c);12⎛1 ⎛ 2 ⎞⎞ ⎛ 1 ⎛ 2 ⎞⎞при a = 1 ; c = – 1 (2 – ac)(a –c), ⎜ 2 − 1 ⋅ ⎜ −1 ⎟ ⎟ ⋅ ⎜1 − ⎜ −1 ⎟ ⎟ =3 ⎝ 3 ⎠⎠ ⎝ 3 ⎝ 3 ⎠⎠33⎝20 ⎞ ⎛ 4 5 ⎞ ⎛ 18 20 ⎞38 ⋅ 32⎛= ⎜2 + ⎟⋅⎜ + ⎟ = ⎜ + ⎟⋅3 == 12 ;9 ⎠ ⎝ 3 3⎠ ⎝ 99 ⎠93⎝б) x2y – y + xy2 – x = xy(x + y) – (x + y) = (x + y)(xy – 1);при x = 4; y = 0,25(x + y)(xy – 1), (4 + 0,25)(4 ⋅ 0,25 – 1) = 4,25 ⋅ 0 = 0.91№763.а) 2,7 ⋅ 6,2 – 9,3 ⋅ 1,2 + 6,2 ⋅ 9,3 – 1,2 ⋅ 2,7 == 2,7(6,2 – 1,2) + 9,3(6,2 – 1,2) = 5(2,7 + 9,3) = 5 ⋅ 12 = 60;б) 1,25⋅14,9+0,75⋅1,1+14,9⋅0,75 + 1,1⋅1,25=1,25(4,9 + 1,1)+0,75(1,1+14,9) == 1,25 ⋅ 16 + 0,75 ⋅ 16 = 16(1,25 + 0,75) = 16 ⋅ 2 = 32;№764.а) ac2 – ad + c3 – cd – bc2 + bd = c2(a + c) – d(a + c) – b(c2 – d) == (a + c)(c2 – d) – b(c2 – d) = (c2 – d)(a + c – b);б) ax2 + ay2 – bx2 – by2 + b – a = a(x2 + y2) – b(x2 + y2) – (a – b) == (x2 + y2)(a – b) – (a – b) = (a – b)(x2 + y2 – 1);в) an2+cn2–ap+ap2–cp+cp2 = n2(a+c)–p(a+ c)+ p2(a + c)=(a + c)(n2 – p + p2);г) xy2–by2 – ax + ab + y2 – a = y2(x – b + 1) – a(x – b + 1)=(x – b + 1)(y2 – a).№765.

а) x2y + x + xy2 + y + 2xy + 2 = xy(x + y) + (x + y) + 2(xy + 1) == (x + y)(xy + 1) = 2(xy + 1) = (xy + 1)(x + y + 2);б) x2 – xy + x – xy2 + y3 – y2 = x(x – y + 1) – y2(x – y + 1)=(x – y + 1)(x – y2).№766. а) x2 + 6x + 5 = x2 + x+ 5x + 5 = x(x + 1) + 5(x + 1) = (x + 1)(x + 5);б) x2 – x – 6 = x2 – 3x + 2x – 6 = x(x – 3) + 2(x – 3) = (x – 3)(x + 2).№767. Если в стаде было x голов, то (x + 60) голов стало. 12,8x л — получали молока в 1 день; 15(x + 60) л стали получать в день.

Это на 1340 лбольше, чем 12,8x л, значит:15(x + 60) – 12,8x = 1340, 15x + 900 – 12,8x = 1340, 2,2x = 440,x = 200 голов было, 260 голов стало.Ответ: 260.№768. Если по плану надо было изготовить x изделий в час, то 9x + 6) изделий в час бригада изготавливала на самом деле. По условию 6 ⋅ (x + 6) изделий изготовили. Это составило 120% дневной нормы от 8x изделий.

8x —100%, 6x + 36 — 120%,8x ⋅ 120 = 100(6x + 36), 4x ⋅ 2 = 5(x + 6), 8x – 5x = 30, 3x = 30,x = 10 изделий бригада должна была изготавливать.Ответ: 10 изделий.№769.а) 4 – x(x + 8) = 11 – x2, 4 – x2 – 8x = 11 – x2, 8x = –7, x = –0,875;б) 4x(3x–1)–2x(6x+8)=5, 12x2 – 4x – 12x2 – 16x = 5, 20x = – 5, x = –0,25.30.

Доказательство тождеств№770.а) –a(c – b) = – ac + ba = a(b – c);б) m(m – n – k)= – mn – km + m2 = –m(n + k – m);в) (y–x)(b–a)=yb–xb–ay+ax=a(x–y) – b(x – y) = (a –b)(x – y) = (x – y)(a – b);г) (x – a)(y – b)(z – c) = –(a – x)((–(b – y))(–(c – z)) = –(a – x)(b – y)(c – z).№771.а) 2a – 3b = –3b + 2a = –(3b – 2a);б)(2a – 3b)2 = (2a – 3b)(2a – 3b) = 4a2 – 6ab – 6ab + 9b2 = 9b2 – 12ab + 4a2,(3b – 2a)2 = (3b – 2a)(3b – 2a) = 9b2 – 6ab – 6ab + 4a2 = 9b2 – 12ab + 4a2,(2a – 3b)2 = (3b – 2a)2.92№772.а) 10a –(–(5a + 20)) = 10a – (–5a – 20) = 10a + 5a + 20=15a+20=5(3a + 4);б) –(–7x) – (–(6 – 5x)) = 7x – (–6 + 5x) = 7x + 6 – 5x = 2x + 6 = 2(x + 3)в) 12y–(25–(6y–11))=12y–25+(6y–1) = 12y – 25 + 6y – 11=18y–36=18(y–2);г) 47–(3b–(9–5b)) = 47 – 3b + (9 – 5b) = 47 – 3b + 9 – 5b=56–8b = 8(7 – b).№773.а) 1) –x(x – a) (x + b) = x(a – x)(b + x) = x(a – x)(x + b) = (ax – x2)(x + b) == x2 + abx – bx2 – x3;2) x(a – x)(b + x) = x(ab + ax – bx – x_2_) = abx + ax2 – bx2 – x3ax2 + abx – bx2 – x3 = abx + ax2 – bx2 – x3;б) 1) (–a – b)(a + b) = –a2 – ab – ab – b2 = – a2 – 2ab – b2;2) –(a + b)2 = –(a + b)(a + b) = –(a2 + 2ab + b2) = –a2 – 2ab – b2;в) 36 – (–(9c – 15)) = 36 – (–9c + 15) = 36 + 9c – 15 = 21 + 9c = 3(7 + 3c);г) y(–2 – (y – 4)) = y(–2 – y + 4) = y(2 – y).№774.а) a(b – x) + x(a + b) = ab – ax + ax + bx = ab + bx = b(a + x);б) c(y – 2) + 2(y + c) = cy – 2c + 2y + 2c = cy + 2y = y(c + 2);в) a(a – b) + 2ab = a2 – ab + 2ab = a2 + ab = a(a + b);г) x(1 – x) +x(x2 – 1) = x – x2 + x3 – x = x2(x – 1).№775.KBCmaALbNnMDSABKLMD = SABCD – SKCML = ab – mn илиSABKLMD = SABKN + SKLMD = (b – n)a + (a – m)n,(b – n)a + (a – m)n = ab – mn.№776.

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