Question

Phan tích : \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

Answer 1

Ta có:

\(A=\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

\(\Rightarrow\sqrt{2}A=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}\)

\(=\sqrt{7}-1-\left(\sqrt{7}+1\right)\) \(=-2\)

\(\Rightarrow A=-\sqrt{2}\)

Answer 2

ta có:

\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

\(=\dfrac{\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{7}-1-\sqrt{7}-1}{\sqrt{2}}\)

\(=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)

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