Question

C/m: \(\sqrt{11+6\sqrt{2}}\) + \(\sqrt{11-6\sqrt{2}}\) = 6

Answer 1

Ta có VT:

\(VT=\sqrt{11+6\sqrt{2}}+\sqrt{11-6\sqrt{2}}\)

\(=\sqrt{3^2+2\cdot3\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}+\sqrt{3^2-2\cdot3\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}\)

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

\(=\left|3+\sqrt{2}\right|+\left|3-\sqrt{2}\right|\)

\(=3+\sqrt{2}+3-\sqrt{2}\)

\(=6=VP\left(dpcm\right)\)

Answer 2

\(VT=\sqrt{9+2\cdot3\cdot\sqrt{2}+2}+\sqrt{9-2\cdot3\cdot\sqrt{2}+2}\)

\(=3+\sqrt{2}+3-\sqrt{2}\)

=6=VP