Question

Câu 1: Rút gọn biểu thức:

a) \(\sqrt{19+\sqrt{136}}-\sqrt{19-\sqrt{136}}\)

b) \(\sqrt{27}+\sqrt{-64}+2\sqrt{125}\)

Câu 2: Tìm x biết:

\(\sqrt{4x+20}-2\sqrt{x+5}+\sqrt{9x+45}=6\)

Answer 1

a) \(\sqrt{19+\sqrt{136}}\) -\(\sqrt{19-\sqrt{136}}\)
= \(\sqrt{19+2\sqrt{34}}\) - \(\sqrt{19-2\sqrt{34}}\)
= \(\sqrt{\left(\sqrt{17}+\sqrt{2}\right)^2}\) - \(\sqrt{\left(\sqrt{17}-\sqrt{2}\right)^2}\)
= \(\left|\sqrt{17}+\sqrt{2}\right|-\left|\sqrt{17}-\sqrt{2}\right|\)
= \(\sqrt{17}+\sqrt{2}-\sqrt{17}+\sqrt{2}\)
= \(2\sqrt{2}\)