a: ĐKXĐ: 1-x>0 và 1+x>0
=>x<1 và x>-1
=>-1<x<1
b: \(L=\left(\frac{1}{\sqrt{1-x}}+\frac{1}{\sqrt{1+x}}\right)^2\cdot\frac{x^2-1}{2}-\sqrt{1-x^2}\)
\(=\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{\left(1+x\right)\left(1-x\right)}}\right)^2\cdot\frac{x^2-1}{2}-\sqrt{1-x^2}\)
\(=\frac{1+x+1-x+2\cdot\sqrt{\left(1+x\right)\left(1-x\right)}}{1-x^2}\cdot\frac{x^2-1}{2}-\sqrt{1-x^2}\)
\(=\frac{2+2\cdot\sqrt{1-x^2}}{1}\cdot\frac{-1}{2}-\sqrt{1-x^2}=-1-\sqrt{1-x^2}-\sqrt{1-x^2}=-2\cdot\sqrt{1-x^2}-1\)
c: L=-2
=>\(-2\cdot\sqrt{1-x^2}-1=-2\)
=>\(-2\cdot\sqrt{1-x^2}=-1\)
=>\(\sqrt{1-x^2}=\frac12\)
=>\(1-x^2=\frac14\)
=>\(x^2=1-\frac14=\frac34\)
=>\(\left[\begin{array}{l}x=\frac{\sqrt3}{2}\left(nhận\right)\\ x=-\frac{\sqrt3}{2}\left(nhận\right)\end{array}\right.\)
