Question

Tìm x biết:

\(\dfrac{2}{3}\)\(\sqrt{4x^2-20}\)+2\(\sqrt{\dfrac{x^2-5}{9}}\)-3\(\sqrt{x^2-5}\)=2

Answer 1

\(\dfrac{2}{3}\sqrt{4x^2-20}+2\sqrt{\dfrac{x^2-5}{9}}-3\sqrt{x^2-5}=2\)

\(\Leftrightarrow\dfrac{2}{3}.2\sqrt{x^2-5}+2\dfrac{\sqrt{x^2-5}}{3}-3\sqrt{x^2-5}=2\)

\(\Leftrightarrow\dfrac{4}{3}\sqrt{x^2-5}+\dfrac{2}{3}\sqrt{x^2-5}-3\sqrt{x^2-5}=2\)

\(\Leftrightarrow\left(\dfrac{4}{3}+\dfrac{2}{3}-3\right)\sqrt{x^2-5}=2\)

\(\Leftrightarrow-\sqrt{x^2-5}=2\)

Vì \(-\sqrt{x^2-5}\) \(\le\)0 nên mình nghĩ phương trình vô \(\eta\) nhé :))

Answer 2

\(\dfrac{2}{3}\sqrt{4x^2-20}+2\sqrt{\dfrac{x^2-5}{9}}-3\sqrt{x^2-5}=2\)

\(\Leftrightarrow\dfrac{4}{3}\sqrt{x^2-5}+\dfrac{2}{3}\sqrt{x^2-5}-3\sqrt{x^2-5}=2\)

\(\Leftrightarrow-\sqrt{x^2-5}=2\Leftrightarrow x^2=9\Leftrightarrow x=\pm3\)