Question

СРОЧНО!!!!!!!!!!! ДАМ 55 БАЛЛОВ!!!!!!!!!!!!!!!! ЗАДАНИЕ ПРИКРЕПЛЕНО НИЖЕ!!!!!!!!!!!

Answer 1

1)

${x}^{4} + 2 {x}^{2} - 24 = 0 \\ {x}^{2} = a \: , \: \: a \geqslant 0 \\ {a}^{2} + 2a - 24 = 0$

По теореме Виета:

${x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c$

$a_{1} + a_{2} = - 2\\ a_{1}a_{2} = - 24 \\ a_{1} = - 6\\ a_{2} = 4$

Первый корень не подходит

${x}^{2} = 4 \\ {x}^{2} - 4 = 0 \\ (x - 2)( x+ 2) = 0 \\ x_{1} = 2 \\ x_{2} = - 2$

2)

$x - 5 \sqrt{x} - 50 = 0 \\ \sqrt{x} = a \: ,\: \: a \geqslant 0 \\ {a}^{2} - 5a - 50 = 0$

По теореме Виета:

$a_{1} + a_{2} = 5\\ a_{1}a_{2} = - 50 \\ a_{1} = 10\\ a_{2} = - 5$

Второй корень не подходит.

$\sqrt{x} = 10 \\ x = 100$

3)

$ODZ \: \: \: \: \: \: \: x\neq - 8 \\ \frac{2 {x}^{2} + 6 }{x + 8} = \frac{13x}{x + 8} \\ 2 {x}^{2} + 6 = 13x \\ 2 {x}^{2} - 13 x+ 6 = 0 \\ a = 2 \\ b = - 13 \\ c = 6\\ D = {b}^{2} - 4ac = ( - 13) {}^{2} - 4 \times 2 \times 6 = \\ = 169 - 48 = 121 \\ x_{1} = \frac{13 - 11}{2 \times 2} = \frac{2}{4} = 0.5 \\ x_{2} = \frac{13 + 11}{2 \times 2} = \frac{24}{4} = 6$

4)

$ODZ \: \: \: \: \: \: x\neq - 2 \: \: \: \: \: \: x\neq2 \\ \frac{x}{x + 2} + \frac{x + 2}{x - 2} = \frac{16}{ {x}^{2} - 4} \\ \frac{x}{x + 2} + \frac{x + 2}{x - 2} - \frac{16}{(x - 2)(x + 2)} = 0 \\ \frac{x(x - 2) + (x + 2) {}^{2} - 16}{(x - 2)(x + 2)} = 0 \\ {x}^{2} - 2x + {x}^{2} + 4x + 4 - 16 = 0 \\ 2 {x }^{2} + 2x - 12 = 0 \\ {x}^{2} + x - 6 = 0$

По теореме Виета:

$x_{1} + x_{2} = - 1 \\ x_{1} x_{2} = - 6 \\ x_{1} = - 3 \\ x_{2} = 2$

Второй корень не подходит.

Ответ: х = - 3