Question

Решите уравнения ,используя введение новой переменной:

Answer 1

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

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