Question

\(\sqrt{4-\sqrt{10+2\sqrt{5}}}+\sqrt{4+\sqrt{10+2\sqrt{5}}}\)

Answer 1

bấm máy là ra sao phải mò mẫm 

Answer 2

Đặt \(a=\sqrt{4-\sqrt{10+2\sqrt{5}}};b=\sqrt{4+\sqrt{10+2\sqrt{5}}}\)(a; b >0)

Xét (a + b)²= a² + b² + 2ab

                  = \(4-\sqrt{10+2\sqrt{5}}+4+\sqrt{10+2\sqrt{5}}\)+ 

                                                                        \(2.\sqrt{\left(4-\sqrt{10+2\sqrt{5}}\right)\left(4+\sqrt{10+2\sqrt{5}}\right)}\)

= \(8+2.\sqrt{6-2\sqrt{5}}=8+2.\sqrt{\left(\sqrt{5}-1\right)^2}=8+2\left(\sqrt{5}-1\right)=6+2\sqrt{5}\)

= \(\left(\sqrt{5}+1\right)^2\)=> a + b = \(\sqrt{5}+1\)