Question

Chứng minh:

2\(\sqrt{2}\)(\(\sqrt{3}\)-2)+(1+2\(\sqrt{2}\))\(^2\)-2\(\sqrt{6}\)=9

Answer 1

Có:

\(VT:2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\)

\(=2\sqrt{6}-4\sqrt{2}+1+4\sqrt{2}+4\cdot2-2\sqrt{6}\)

\(=1+8=9=VP\)

=>đpcm

Answer 2

Ta có : \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=2\sqrt{6}-4\sqrt{2}+1+8+4\sqrt{2}-2\sqrt{6}=9\)