ГДЗ учебник по алгебре 7 класс Мерзляк Номер 450

Решите уравнение, используя разложение на множители:
1) (2x − 9)(x + 6) − x(x + 6) = 0;
2) (3x + 4)(x − 10) + (10 − x)(x − 8) = 0;
3)

3 (3 x + 1)^{2} - 4 (3 x + 1) = 0

;
4) (9x − 12) − x(9x − 12) = 0.

(2x − 9)(x + 6) − x(x + 6) = 0
(x + 6)(2x − 9 − x) = 0
(x + 6)(x − 9) = 0

x_{1} + 6 = 0 : (x - 9)

x_{1} + 6 = 0

x_{1} = - 6

;

x_{2} - 9 = 0 : (x + 6)

x_{2} - 9 = 0

x_{2} = 9

.

(3x + 4)(x − 10) + (10 − x)(x − 8) = 0
(3x + 4)(x − 10) − (x − 10)(x − 8) = 0
(x − 10)(3x + 4 − x + 8) = 0
(x − 10)(2x + 12) = 0

x_{1} - 10 = 0 : (2 x + 12)

x_{1} - 10 = 0

x_{1} = 10

;

2 x_{2} + 12 = 0 : (x - 10)

2 x_{2} + 12 = 0

2 x_{2} = - 12

x_{2} = - 12 : 2

x_{2} = - 6

.

3 (3 x + 1)^{2} - 4 (3 x + 1) = 0

(3x + 1)(3(3x + 1) − 4) = 0
(3x + 1)(9x + 3 − 4) = 0
(3x + 1)(9x − 1) = 0

3 x_{1} + 1 = 0 : (9 x - 1)

3 x_{1} + 1 = 0

3 x_{1} = - 1

x_{1} = - \frac{1}{3}

;

9 x_{2} - 1 = 0 : (3 x + 1)

9 x_{2} - 1 = 0

9 x_{2} = 1

x_{2} = \frac{1}{9}

.

(9x − 12) − x(9x − 12) = 0
(9x − 12)(1 − x) = 0

9 x_{1} - 12 = 0 : (1 - x)

9 x_{1} - 12 = 0

9 x_{1} = 12

x_{1} = \frac{12}{9} = \frac{4}{3} = 1 \frac{1}{3}

;

1 - x_{2} = 0 : (9 x - 12)

1 - x_{2} = 0

- x_{2} = - 1

x_{2} = 1

.

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир