Question

Помоги с решением(уравнения) на фото

Answer 1

$\frac{1}{(x-5)^2}-\frac{1}{x-5}-6=0 \\ \\ \frac{1-(x-5)}{(x-5)^2}=6 \\ \\ \frac{1-x+5}{(x-5)^2}=6 \\ \\ \frac{6-x}{(x-5)^2}=6 \\ \\ 6-x=6\cdot (x-5)^2 \\ \\ 6-x = 6\cdot (x^2-2\cdot 5 \cdot x +5^2) \\ \\ 6-x=6x^2-60x+150 \\ \\ 6x^2-59x+144=0 \\ \\ x_{1,2}=\frac{-(-59)\pm \sqrt{(-59)^2-4\cdot 6\cdot 144}}{2\cdot 6}=\frac{59\pm\sqrt{3481-3456}}{12}=\frac{59\pm\sqrt{25}}{12} \frac{59\pm5}{12} \\ \\ x_1=\frac{59+5}{12}=\frac{64}{12}=\frac{16}{3}=5\frac{ 1 }{3};\\\\x_2=\frac{59-5}{12}=\frac{54}{12}=\frac{9}{2}$