Question

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Answer 1

\(\dfrac{\sqrt[4]{86-14\sqrt{37}}}{\sqrt{9-2\sqrt{4+2\sqrt{3}}}-\sqrt{6+\sqrt{13+4\sqrt{3}}}}\)

\(=\dfrac{\sqrt{7-\sqrt{37}}}{\sqrt{9-2\left(\sqrt{3}+1\right)}-\sqrt{6+\left(2\sqrt{3}+1\right)}}\)

\(=\dfrac{\sqrt{7-\sqrt{37}}}{\sqrt{7-2\sqrt{3}}-\sqrt{7+2\sqrt{3}}}\)

\(=\dfrac{\sqrt{7-\sqrt{37}}\cdot\left(\sqrt{7-2\sqrt{3}}+\sqrt{7+2\sqrt{3}}\right)}{7-2\sqrt{3}-7-2\sqrt{3}}\)

\(=-\dfrac{\sqrt{7-\sqrt{37}}\cdot\left(\sqrt{7-2\sqrt{3}}+\sqrt{7+2\sqrt{3}}\right)}{4\sqrt{3}}\)

Tới đây chịu nha