\(\sqrt{12-\frac{12}{x^2}}+\sqrt{x^2-\frac{12}{x^2}}=x^2\)
\(pt\Leftrightarrow\sqrt{12-\frac{12}{x^2}}-3+\sqrt{x^2-\frac{12}{x^2}}-1=x^2-4\)
\(\Leftrightarrow\frac{12-\frac{12}{x^2}-9}{\sqrt{12-\frac{12}{x^2}}+3}+\frac{x^2-\frac{12}{x^2}-1}{\sqrt{x^2-\frac{12}{x^2}}+1}=x^2-4\)
\(\Leftrightarrow\frac{\frac{3x^2-12}{x^2}}{\sqrt{12-\frac{12}{x^2}}+3}+\frac{\frac{x^4-x^2-12}{x^2}}{\sqrt{x^2-\frac{12}{x^2}}+1}-\left(x^2-4\right)=0\)
\(\Leftrightarrow\frac{\frac{3\left(x-2\right)\left(x+2\right)}{x^2}}{\sqrt{12-\frac{12}{x^2}}+3}+\frac{\frac{\left(x-2\right)\left(x+2\right)\left(x^2+3\right)}{x^2}}{\sqrt{x^2-\frac{12}{x^2}}+1}-\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(\frac{\frac{3}{x^2}}{\sqrt{12-\frac{12}{x^2}}+3}+\frac{\frac{x^2+3}{x^2}}{\sqrt{x^2-\frac{12}{x^2}}+1}-1\right)=0\)
SUy ra x=±2
\(\sqrt{x^2}\)+\(\sqrt{x^2+3}\)+\(2x^2\)+3+2\(\sqrt{x^2\left(x^2+3\right)}\)=12
Đặt \(\sqrt{x^2}\)+\(\sqrt{x^2+3}\)=a (a>0)
=> \(2x^2\)+3+2\(\sqrt{x^2\left(x^2+3\right)}\)= \(a^2\)
Chị QA 114 đấy
