Question

Chứng minh \(\left(x\sqrt{\frac{6}{x}}+\sqrt{\frac{2x}{3}}+\sqrt{6x}\right):\sqrt{6}=2\frac{1}{3}\) : 

Answer 1

\(\left(x\sqrt{\frac{6}{x}}+\sqrt{\frac{2x}{3}}+\sqrt{6x}\right):\sqrt{6x}=2\frac{1}{3}\)

Answer 2

\(\left(x\sqrt{\frac{6}{x}}+\sqrt{\frac{2x}{3}}+\sqrt{6x}\right):\sqrt{6x}=2\frac{1}{3}\)    \(\left(x>0\right)\)

\(VT=\left(x\sqrt{\frac{6}{x}}+\sqrt{\frac{2x}{3}}+\sqrt{6x}\right):\sqrt{6x}\)

\(=\left(\sqrt{x^2.\frac{6}{x}}+\sqrt{\frac{6x}{3^2}}+\sqrt{6x}\right):\sqrt{6x}\)

\(=\left(\sqrt{6}+\frac{\sqrt{6x}}{3}+\sqrt{6x}\right):\sqrt{6x}\)

\(=\frac{7}{3}\sqrt{6x}\div\sqrt{6}\)

\(=\frac{7}{3}=2\frac{1}{3}\)

\(=VP\left(\text{đ}pcm\right)\)