Question

Gỉai  phương trinfnh : 

A= \(\left(x-2\right)\left(x+2\right)+4\left(x-2\right)\sqrt{\frac{x+2}{x-2}}=-3\)

Answer 1

\(\text{Đ}K:x>2\) hoặc \(x\le-2\)

\(A=\left(x+2\right)\left(x-2\right)+4\left(x-2\right)\sqrt{\frac{x+2}{x-2}}=-3\)

\(A=\left(x^2-4\right)+4.\sqrt{x-2}.\sqrt{x+2}=-3\)

\(A=\left(x^2-4\right)+4\sqrt{x^2-4}=-3\)

\(A=\sqrt{x^2-4}\left(1-4\right)=-3\)

\(A=\sqrt{x^2-4}.\left(-3\right)=-3\)

\(A=\sqrt{x^2-4=1}\)

\(A=x^2-4=1\)

\(A=x^2=5\)

\(A=x=\orbr{\begin{cases}\sqrt{5}\\-\sqrt{5}\end{cases}}\)

Vây \(x=\orbr{\begin{cases}-\sqrt{5}\\\sqrt{5}\end{cases}}\)