Question

Giải pt: \(\sqrt{x^2-\frac{7}{x^2}}+\sqrt{x-\frac{7}{x^2}}=x\)

Answer 1

\(\sqrt{x^2-\frac{7}{x^2}}+\sqrt{x-\frac{7}{x^2}}=x\)

\(\Leftrightarrow\sqrt{x^2-\frac{7}{x^2}}+\sqrt{x-\frac{7}{x^2}}-\sqrt{x-\frac{7}{x^2}}=x-\sqrt{x-\frac{7}{x^2}}\)

\(\Leftrightarrow\left(\sqrt{x^2-\frac{7}{x^2}}\right)^2=\left(x-\sqrt{x-\frac{7}{x^2}}\right)^2\)

\(\Leftrightarrow x^2-\frac{7}{x^2}=x^2-2\sqrt{x-\frac{7}{x^2}}.x+x-\frac{7}{x^2}\)

\(\Leftrightarrow2\sqrt{x-\frac{7}{x^2}}.x-x=0\)

\(\Leftrightarrow x\left(2\sqrt{x-\frac{7}{x^2}}-1=0\right)\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\left(ktm\right)\\x=2\left(tm\right)\end{cases}}\)

=> x = 2