Question

√(12+х) -√(7х+8)=-2 . Решите пожалуйста !!!

Answer 1

$\sqrt{12 + x} - \sqrt{7x + 8} = -2\\\sqrt{12 + x} = \sqrt{7x + 8} - 2\\(\sqrt{12 + x})^{2} = (\sqrt{7x + 8} - 2)^{2}\\12 + x = 7x + 8 - 4\sqrt{7x + 8} + 4\\6x = 4\sqrt{7x + 8} \ \ \ \ \\3x = 2\sqrt{7x + 8}\\(3x)^{2} = (2\sqrt{7x + 8})^{2}\\9x^{2} = 4(7x + 8)\\9x^{2} = 28x + 32\\9x^{2} - 28x - 32 = 0\\x_{1}= -\dfrac{8}{9}\\x_{2} = 4$

Проверка:

$x = -\dfrac{8}{9}: \ \sqrt{12 -\dfrac{8}{9}} - \sqrt{-\dfrac{7 \cdot 8}{9} + 8} = 2$

$x = 4: \ \sqrt{12 + 4} - \sqrt{7 \cdot 4 + 8} = -2$

Ответ: 4