Решите уравнение:
1)

(x + 9)^{2} - x (x + 8) = 1

;
2)

(x - 11)^{2} = (x - 7) (x - 9)

;
3)

(x - 4) (x + 4) - (x + 6)^{2} = - 16

;
4)

(1 - 3 x)^{2} - x (9 x - 2) = 5

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Алгебре 7 класс Мерзляк. Номер №574

(x + 9)^{2} - x (x + 8) = 1

x^{2} + 18 x + 81 - x^{2} - 8 x = 1

18x − 8x = 1 − 81
10x = −80
x = −80 : 10
x = −8

(x - 11)^{2} = (x - 7) (x - 9)

x^{2} - 22 x + 121 = x^{2} - 7 x + 63 - 9 x

x^{2} - x^{2} - 22 x + 7 x + 9 x = 63 - 121

−22x + 7x + 9x = −58
−6x = −58

x = \frac{58}{6} = \frac{29}{3} = 9 \frac{2}{3}

(x - 4) (x + 4) - (x + 6)^{2} = - 16

x^{2} - 16 - (x^{2} + 12 x + 36) = - 16

x^{2} - 16 - x^{2} - 12 x - 36 = - 16

−12x = −16 + 16 + 36
−12x = 36
x = 36 : −12
x = −3

(1 - 3 x)^{2} - x (9 x - 2) = 5

1 - 6 x + 9 x^{2} - 9 x^{2} + 2 x = 5

−6x + 2x = 5 − 1
−4x = 4
x = 4 : (−4)
x = −1

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир