Question

Tìm x: 

\(\left(\frac{x}{x-1}\right)^2\)+ \(\left(\frac{x}{x+1}\right)^2\)= \(\frac{10}{9}\)

Answer 1

\(\Leftrightarrow\frac{2x^4+2x^2}{\left(x^2-1\right)^2}=\frac{10}{9}\Rightarrow18x^4+18x^2=10x^4-20x^2+10\)

\(\Rightarrow8x^4+38x^2-10=0\Rightarrow2\left(4x^2-1\right)\left(x^2+5\right)=0\)

\(\Rightarrow\left(4x^2-1\right)\left(x^2+5\right)=0\)

\(\Rightarrow4x^2-1=0\Rightarrow4x^2=1\Rightarrow x^2=\frac{1}{4}\Rightarrow x=+-\frac{1}{2}\)

hoặc \(x^2+5=0\Rightarrow x^2=-5\)(vô lý)

Vậy x = -1/2 ; x = 1/2