Question

Giải phương trình

\(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)

Answer 1

pt nào z bn?

\(=\left(3+2\sqrt{3\cdot2}+2\right)\left(25-2\cdot5\cdot2\sqrt{6}+24\right)\sqrt{3-2\sqrt{6}+2}\)

\(=\left(\sqrt{3}+\sqrt{2}\right)^2\left(5-2\sqrt{6}\right)^2\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)

\(=\left(\sqrt{3}+\sqrt{2}\right)^2\left(\sqrt{3}-\sqrt{2}\right)^4\left(\sqrt{3}-\sqrt{2}\right)\)

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

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