Question

x/ x²-25 + 4-x/ x-5 = 0 решите уравнение

Answer 1

Ответ: -2√5; 2√5

Объяснение:

$\frac{x}{x^2-25}+\frac{4-x}{x-5}=0\\ \\ \frac{x}{(x-5)(x+5)}+\frac{4-x}{x-5}=0\\ \\ \frac{x+(4-x)(x+5)}{(x-5)(x+5)}=0\\ \\ \frac{x+4x-x^2+20-5x}{(x-5)(x+5)}=0\\ \\\frac{-x^2+20}{(x-5)(x+5)}=0\\ \\ \left \{ {{20-x^2=0,} \atop {(x-5)(x+5)\neq 0}} \right. \\\\  \left\{\begin{matrix}20-x^2=0,\\ x-5\neq 0,\\ x+5\neq 0\end{matrix}\right.$

$\left\{\begin{matrix}x^2=20,\\ x\neq 5,\\ x\neq -5\end{matrix}\right.$

$\left\{\begin{matrix}x=б\sqrt{20},\\ x\neq 5,\\ x\neq -5\end{matrix}\right.$

$\left\{\begin{matrix}x=б2\sqrt{5},\\ x\neq 5,\\ x\neq -5\end{matrix}\right.$