Question

\(\left(\frac{x}{x+1}\right)^4-\left(\frac{x}{x+1}\right)^2=\frac{3}{2}\)

Answer 1

Đặt t=\(\left(\frac{x}{x+1}\right)^2\) (t>0)

Có: t²-t-\(\frac{3}{2}\)=0

\(\Leftrightarrow\left[{}\begin{matrix}t=\frac{1+\sqrt{7}}{2}\left(TM\right)\\t=\frac{1-\sqrt{7}}{2}\left(KTM\right)\end{matrix}\right.\)

\(\Rightarrow\left(\frac{x}{x+1}\right)^2=\frac{1+\sqrt{7}}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}\frac{x}{x+1}=\sqrt{\frac{1+\sqrt{7}}{2}}\\\frac{x}{x+1}=-\sqrt{\frac{1+\sqrt{7}}{2}}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\sqrt{\frac{1+\sqrt{7}}{2}}}{1-\sqrt{\frac{1+\sqrt{7}}{2}}}\\x=\frac{-\sqrt{\frac{1+\sqrt{7}}{2}}}{1+\sqrt{\frac{1+\sqrt{7}}{2}}}\end{matrix}\right.\)

Bạn tham khảo nha