Question

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Answer 1

\(N=1+\left|1-\sqrt{2}\right|+\dfrac{2\sqrt{2}}{2}=1+\sqrt{2}-1+\sqrt{2}=2\sqrt{2}\)

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

\(M+N=2\sqrt{2}+2\sqrt{2}=4\sqrt{2}\)

\(F=\left(\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right).\dfrac{\sqrt{x}-2}{\sqrt{x}}\)

\(=\dfrac{2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\sqrt{x}-2}{\sqrt{x}}=\dfrac{2}{\sqrt{x}+2}\)