Question

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Answer 1

ĐKXĐ: \(x\ge\sqrt{5}\)

\(\sqrt{x^2-1}-\sqrt{x+5}+\sqrt{x^2-3}-\sqrt{x+3}+\sqrt{x^2-5}-\sqrt{x+1}=0\)

\(\Leftrightarrow\dfrac{x^2-x-6}{\sqrt{x^2-1}+\sqrt{x+5}}+\dfrac{x^2-x-6}{\sqrt{x^2-3}+\sqrt{x+3}}+\dfrac{x^2-x-6}{\sqrt{x^2-5}+\sqrt{x+1}}=0\)

\(\Leftrightarrow\left(x^2-x-6\right)\left(\dfrac{1}{\sqrt{x^2-1}+\sqrt{x+5}}+\dfrac{1}{\sqrt{x^2-3}+\sqrt{x+3}}+\dfrac{1}{\sqrt{x^2-5}+\sqrt{x+1}}\right)=0\)

\(\Leftrightarrow x^2-x-6=0\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\left(loại\right)\end{matrix}\right.\)