Решебник по алгебре 7 класс Мерзляк Задание 574

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Пояснение.

Решение.

\[1)\ (x + 9)^{2} - x \cdot (x + 8) = 1\]

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

\[10x = - 80\]

\[x = - 8\]

\[Ответ:\ x = - 8.\]

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

\[x^{2} - 22x + 121 =\]

\[= x^{2} - 9x - 7x + 63\]

\[- 6x = - 58\]

\[x = \frac{58}{6} = 9\frac{2}{3}\]

\[Ответ:x = 9\frac{2}{3}.\]

\[3)\ (x - 4)(x + 4) - (x + 6)^{2} =\]

\[= - 16\]

\[x^{2} - 16 - x^{2} - 12x - 36 = - 16\]

\[- 12x = 36\]

\[x = - 3\]

\[Ответ:\ x = - 3.\]

\[4)\ (1 - 3x)^{2} - x(9x - 2) = 5\]

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

\[- 4x = 4\]

\[x = - 1\]

\[Ответ:\ x = - 1.\]