Question

Chứng minh rằng:  \(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}=\frac{-3}{2}\)

Answer 1

có VT \(=\left(\frac{\sqrt{3}\left(2-\sqrt{2}\right)}{\sqrt{2}\left(2-\sqrt{2}\right)}-\frac{6\sqrt{6}}{3}\right).\frac{1}{\sqrt{6}}=\left(\frac{\sqrt{3}}{\sqrt{2}}-2\sqrt{6}\right).\frac{1}{\sqrt{6}}=\frac{-3\sqrt{3}}{\sqrt{2}}.\frac{1}{\sqrt{6}}=\frac{-3}{2}\)

dpcm

Answer 2

Ta có: \(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)

  \(=\left\{\left[\frac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}\right]-\frac{6\sqrt{6}}{3}\right\}\times\frac{1}{\sqrt{6}}\)

  \(=\left(\frac{\sqrt{6}}{2}-2\sqrt{6}\right)\times\frac{1}{\sqrt{6}}\)

  \(=\left(-\frac{3\sqrt{6}}{2}\right)\times\frac{1}{\sqrt{6}}\)

  \(=\frac{-3}{2}\)(đpcm)