Question

Giải pt sau :

\(x^2-1+\sqrt{143}=\frac{1}{x^2-1}-\sqrt{143}\)

Answer 1

\(x^2-1+\sqrt{143}=\frac{1}{x^2-1}-\sqrt{143}\)(đk: \(x\ne1\))

Đặt \(x^2-1=a\left(a\ge-1,a\ne0\right)\)

Có \(a+\sqrt{143}=\frac{1}{a}-\sqrt{143}\)

<=> \(a-\frac{1}{a}+2\sqrt{143}=0\)

<=> \(\frac{a^2-1+2\sqrt{143}a}{a}=0\)

<=> \(a^2+2\sqrt{143}a+143=144\)

<=> \(\left(a+\sqrt{143}\right)^2=144\)

=> \(\left[{}\begin{matrix}a+\sqrt{143}=12\\a+\sqrt{143}=-12\left(ktm\right)\end{matrix}\right.\) <=> \(a=12-\sqrt{143}\)

<=> \(x^2-1=12+\sqrt{143}\)

Làm nốt nha :))