Решите уравнение:
1)

8 x^{2} - 3 (x - 4) = 12

;
2)

5 x^{3} - x (2 x - 3) = 3 x

;
3)

4 x - 0, 2 x (x + 20) = x^{3}

;
4) 9x(x − 3) + (x − 4)(x − 5) = 20.

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Алгебре 7 класс Мерзляк. Номер №457

8 x^{2} - 3 (x - 4) = 12

8 x^{2} - 3 x + 12 = 12

8 x^{2} - 3 x = 12 - 12

8 x^{2} - 3 x = 0

x (8 x - 3) = 0

x_{1} = 0 : (8 x - 3)

x_{1} = 0

;

8 x_{2} - 3 = 0 : x

8 x_{2} - 3 = 0

8 x_{2} = 3

x_{2} = \frac{3}{8}

5 x^{3} - x (2 x - 3) = 3 x

5 x^{3} - 2 x^{2} + 3 x = 3 x

5 x^{3} - 2 x^{2} + 3 x - 3 x = 0

5 x^{3} - 2 x^{2} = 0

x^{2} (5 x - 2) = 0

x^{2} = 0 : (5 x - 2)

x^{2} = 0

x_{1} = 0

;

5 x_{2} - 2 = 0 : x^{2}

5 x_{2} - 2 = 0

5 x_{2} = 2

x_{2} = \frac{2}{5}

4 x - 0, 2 x (x + 20) = x^{3}

4 x - 0, 2 x^{2} - 4 x = x^{3}

- 0, 2 x^{2} = x^{3}

- x^{3} - 0, 2 x^{2} = 0

- x^{2} (x + 0, 2) = 0

- x^{2} = 0 : (x + 0, 2)

- x^{2} = 0

x_{1} = 0

;

x_{2} + 0, 2 = 0 : (- x^{2})

x_{2} + 0, 2 = 0

x_{2} = - 0, 2

9x(x − 3) + (x − 4)(x − 5) = 20

9 x^{2} - 27 x + x^{2} - 4 x - 5 x + 20 = 20

10 x^{2} - 36 x = 20 - 20

2 x (5 x - 18) = 0

2 x_{1} = 0 : (5 x - 18)

2 x_{1} = 0

x_{1} = 0

;

5 x_{2} - 18 = 0 : 2 x

5 x_{2} - 18 = 0

5 x_{2} = 18

x_{2} = \frac{18}{5} = \frac{36}{10} = 3, 6

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир, 2018