Question

Решите уравнения ,используя введение новой переменной:

Answer 1

$\frac{12}{x^2+x-10} - \frac{6}{x^2+x-6}= \frac{5}{x^2+x-11}\\ zamena\\ x^2+x=a\\ \frac{12}{a-10} - \frac{6}{a-6}= \frac{5}{a-11}\\ \\ \frac{12(a-6)-6(a-10)}{(a-10)(a-6)}= \frac{5}{a-11}\\ \frac{12a-72-6a+60}{(a-10)(a-6)}= \frac{5}{a-11}\\ \frac{6a-12}{(a-10)(a-6)} = \frac{5}{a-11}\\ \frac{(a-11)(6a-12)}{(a-10)(a-6)} = \frac{5(a-10)(a-6)}{(a-11)(a-10)(a-6)}\\ (a-11)(6a-12)=5(a-10)(a-6)\\ a^2+2a-168=0\\ a=12$

$a=-14\\ \\ x^2+x=12\\ x^2+x-12=0\\ D=1+4*1*12 = 7^2\\ x_{1}=\frac{-1+7}{2}=3\\ x_{2}=\frac{-1-7}{2}=-4$