Question

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

Answer 1

ĐK : \(x\ge\sqrt[4]{7}\)

pt <=> \(\sqrt{x^2-\frac{7}{x^2}}=x-\sqrt{x-\frac{7}{x^2}}\)

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

<=> \(x-2x\sqrt{x-\frac{7}{x^2}}=0\)

=> \(x=2x\sqrt{x-\frac{7}{x^2}}\)

=> \(1=2\sqrt{x-\frac{7}{x^2}}\Leftrightarrow1=4\left(x-\frac{7}{x^2}\right)\)

=> \(4x-\frac{28}{x^2}-1=0\)

=> \(4x^3-x^2-28=0\)

=> \(4x^3-8x^2+7x^2-14x+14x-28=0\)

=>  \(\left(x-2\right)\left(4x^2-7x+14\right)=0\)

=> \(x=2\) hoặc \(4x^2-7x+14=0\) 

Tự giải tiếp nha 

Answer 2

x=185...........................