Question

Rút gọn bt A = \(\left(3\sqrt{7}+2\right).\sqrt{67-12\sqrt{17}}\)

Answer 1

Sửa đề: \(A=\left(3\sqrt{7}+2\right)\cdot\sqrt{67-12\sqrt{7}}\)

Ta có: \(A=\left(3\sqrt{7}+2\right)\cdot\sqrt{67-12\sqrt{7}}\)

\(=\left(3\sqrt{7}+2\right)\cdot\sqrt{63-2\cdot3\sqrt{7}\cdot2+4}\)

\(=\left(3\sqrt{7}+2\right)\cdot\sqrt{\left(3\sqrt{7}-2\right)^2}\)

\(=\left(3\sqrt{7}+2\right)\cdot\left|3\sqrt{7}-2\right|\)

\(=\left(3\sqrt{7}+2\right)\left(3\sqrt{7}-2\right)\)(Vì \(3\sqrt{7}>2\))

\(=63-4=59\)