Question

Решите пожалуйста! 279.

Answer 1

279.

$\sqrt{12x {}^{2} + 7x - 10 } - 5 = 4x \\ \sqrt{12x {}^{2} + 7x - 10 } = 4x + 5 \\ 12x {}^{2} + 7x - 10 = (4x + 5) {}^{2} \\ 12 {x}^{2} + 15x - 8x - 10 = (4x + 5) {}^{2} \\ 3x(4x + 5) - 2(4x + 5) = (4x + 5) {}^{2} \\(4x + 5) \times (3x - 2) = (4x + 5) {}^{2} \\ (4x + 5) \times (3x - 2) - (4x + 5) {}^{2} = 0 \\ (4x + 5) \times ((3x - 2) - (4x + 5)) = 0 \\ (4x + 5) \times (3x - 2 - 4x - 5) = 0 \\ (4x + 5) \times ( - x - 7) = 0$

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$4x + 5 = 0 \\ 4x = - 5 \\ x = - \frac{5}{4}$

$- x - 7 = 0 \\ - x = 7 \\ x = - 7$

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Подставим и проверим:

$\sqrt{12 \times ( - \frac{5}{4}) {}^{2} + 7 \times ( - \frac{5}{4}) - 10} - 5 = 4 \times ( - \frac{5}{4} ) \\ - 5 = - 5$

$\sqrt{12 \times ( - 7) {}^{2} + 7 \times ( - 7) - 10} - 5 = 4 \times ( - 7) \\ 18≠ - 28$

Значит

$x = - \frac{5}{4}$

или -1,25.

Ответ: x=-1,25. (-5/4)