X=3-√5 find the value of √x+ 1/√x

1 answer:

5 0

$\bf x = 3-\sqrt{5} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{x}+\cfrac{1}{\sqrt{x}}\implies (3-\sqrt{5})+\cfrac{1}{3-\sqrt{5}}\qquad \impliedby \textit{let use the LCD of }3-\sqrt{5} \\\\\\ \cfrac{(3-\sqrt{5})3-(3-\sqrt{5})\sqrt{5}+(1)1}{3-\sqrt{5}} \implies \cfrac{9-3\sqrt{5}-(3\sqrt{5}-5)+1}{3-\sqrt{5}} \\\\\\ \cfrac{9-3\sqrt{5}-3\sqrt{5}+5+1}{3-\sqrt{5}}\implies \cfrac{15-6\sqrt{5}}{3-\sqrt{5}}$

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