Question

Х^4/(х-2)^2-4х^2/х-2-5=0

Answer 1

$\frac{ {x}^{4} }{(x - 2){}^{2} } - 4\frac{ {x}^{2} }{x - 2} - 5 =0 \\ x - 2≠0 ; \: x≠2 \\ \frac{ {x}^{2} }{x - 2} = t \\ {t}^{2} - 4t - 5 = 0 \\ \left[ \begin{gathered}t_{1} = 5 \\ t_{2} = - 1 \end{gathered} \right. \\ 1) \: \frac{ {x}^{2} }{x - 2} = 5 \\ {x}^{2} = 5x - 10 \\ {x}^{2} - 5x + 10 = 0 \\ D = {5}^{2} - 4 \times 10 < 0 \\ x \in \varnothing \\ 2) \: \frac{ {x}^{2} }{x - 2} = - 1 \\ {x}^{2} = - x + 2 \\ {x}^{2} + x - 2 = 0 \\ \left[ \begin{gathered} x_{1} = 1\\ x_{2} = - 2 \end{gathered} \right.$

Ответ: -2; 1