Question

Cho biểu thức

tính giá trị biểu thức với x=\(-\frac{1}{2017}\)

\(\sqrt{1-X+\left(1-X\right)\sqrt{1-X^2}}+\sqrt{1-X-\left(1-X\right)\sqrt{1-X^2}}\)

Answer 1

\(A=\sqrt{1-x+\left(1-x\right)\sqrt{1-x^2}}+\sqrt{1-x-\left(1-x\right)\sqrt{1-x^2}}\)

\(\Rightarrow A^2=2\left(1-x\right)+2\sqrt{\left(1-x\right)^2-\left(1-x\right)^2\left(1-x^2\right)}\)

\(\Rightarrow A^2=2\left(1-x\right)+2\left(1-x\right)\sqrt{1-\left(1-x^2\right)}\)

\(\Rightarrow A^2=2\left(1-x\right)+2\left(1-x\right)\left|x\right|\)

\(\Rightarrow A^2=2\left(1-x\right)\left(1+\left|x\right|\right)=2\left(1-x\right)\left(1-x\right)\) do \(x< 0\)

\(\Rightarrow A^2=2\left(1-x\right)^2\Rightarrow A=\sqrt{2}\left(1-x\right)=\frac{2018\sqrt{2}}{2017}\)