Question

\(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}+\dfrac{\sqrt{3}-1}{\sqrt{3}+1}-\sqrt{\left(4-\sqrt{5}\right)^2}\)

Answer 1

Giải:

\(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}+\dfrac{\sqrt{3}-1}{\sqrt{3}+1}-\sqrt{\left(4-\sqrt{5}\right)^2}\)

\(\Leftrightarrow\dfrac{\left(\sqrt{3}+1\right)^2}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}+\dfrac{\left(\sqrt{3}-1\right)^2}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}-\left|4-\sqrt{5}\right|\)

\(\Leftrightarrow\dfrac{3+2\sqrt{3}+1}{3-1}+\dfrac{3-2\sqrt{3}+1}{3-1}-4+\sqrt{5}\)

\(\Leftrightarrow\dfrac{3+2\sqrt{3}+1+3-2\sqrt{3}+1}{3-1}-4+\sqrt{5}\)

\(\Leftrightarrow\dfrac{8}{2}-4+\sqrt{5}\)

\(\Leftrightarrow\sqrt{5}\)

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