Question

Розв'яжіть рівняння ​

Answer 1

$x\neq0 \\ ( \frac{ {x}^{2} + 6 }{x} ) {}^{2} + 2( \frac{ {x}^{2} + 6}{x} ) = 35 \\ \frac{ {x}^{2} + 6 }{x} = a \\ {a}^{2} + 2a - 35 = 0 \\ \\ po \: \: \: teoreme \: \: \: vieta \\ {x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c \\ \\ a_{1} + a_{2} = - 2 \\ a_{1} a_{2} = - 35 \\ a_{1} = - 7 \\ a_{2} = 5 \\ \\ 1) \: a = - 7 \\ \frac{ {x}^{2} + 6 }{x} = - 7 \\ {x}^{2} + 6 = - 7x \\ {x}^{2} + 7x + 6 = 0 \\ po \: \: \: teoreme \: \: \: vieta \\ x_{1} + x_{2} = - 7 \\ x_{1} x_{2} = 6 \\ x_{1} = - 1 \\ x_{2} = - 6 \\ \\ 2) \: a = 5 \\ \frac{ {x}^{2} + 6 }{x} = 5 \\ {x}^{2} + 6 = 5x \\ {x}^{2} - 5x + 6 = 0 \\ po \: \: \: teoreme \: \: \: vieta \\ x_{3} + x_{4} =5 \\ x_{3} x_{4} =6 \\ x_{3} =2 \\ x_{4} = 3$