Question

2(x^2+1/x^2)−3(x+1/x)=1 решите уравнение
Срочно !!!

Answer 1

$2(x^2+frac{1}{x^2} )-3(x+frac{1}{x} )=1\ \ 2((x+frac{1}{x} )^2-2)-3(x+frac{1}{x} )=1\ \ x+frac{1}{x}=t\ \ 2(t^2-2)-3t=1\ \ 2t^2-3t-5=0\ \ D=9+4*2*5=49=7^2\ \ t_{1} =(3-7)/4=-1\ \ x+frac{1}{x}=-1;x^2+x+1=0;D=1-4<0;net kornej\ \ t_{2} =(3+7)/4=5/2\ \ x+frac{1}{x}=frac{5}{2} ;2x^2-5x+2=0;D= 25-16=9=3^2\ \ x_{1} =(5+3)/4=2\ \ x_{2} =(5-3)/4=frac{1}{2}$