Question

Розв'язати рівняння, помогите!!!

Answer 1

$x\neq0 \\ ( \frac{ {x}^{2} - 6}{x}) {}^{2} - 4( \frac{ {x}^{2} - 6}{x} ) - 5 = 0 \\ \frac{ {x}^{2} - 6}{x} = a \\ a {}^{2} - 4a - 5 = 0$

По теореме Виета:

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

$a_{1} + a_{2} = 4 \\ a_{1}a_{2} = - 5 \\ a_{1} = - 1 \\ a_{2} = 5$

1) а = - 1 :

$\frac{ {x}^{2} - 6}{x} = - 1 \\ {x}^{2} - 6 = - x \\ {x}^{2} + x - 6 = 0 \\ po \: \: \: teoreme \: \: \: vieta \\ x_{1} + x_{2} = - 1\\ x_{1} x_{2} = - 6 \\ x_{1} = - 3 \\ x_{2} = 2$

2) а = 5 :

$\frac{ {x}^{2} - 6}{x} = 5 \\ {x}^{2} - 6 = 5x \\ {x}^{2} - 5x - 6 = 0 \\ x_{3} + x_{4} =5 \\ x_{3} x_{4} = - 6\\ x_{3} =6 \\ x_{4} = - 1$