Question

If 7Bb%7D" id="TexFormula1" title=" \sqrt{0.3+ \sqrt{0.08} } = \sqrt{a} + \sqrt{b}" alt=" \sqrt{0.3+ \sqrt{0.08} } = \sqrt{a} + \sqrt{b}" align="absmiddle" class="latex-formula"> Then 1/a + 1/b = ....
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Answer 1

$\sqrt{0.3+ \sqrt{0.08} } = \sqrt{a} + \sqrt{b} \\ \\ \sqrt{0.3+ \sqrt{0.08} } \\ = \sqrt{0.3+ \sqrt{4\times0,02} } \\ = \sqrt{0.3 +2 \sqrt{0.02} } \\ \\ (a+b)^2=a^2+b^2+2ab\\ \\ \sqrt{ (\sqrt{a} + \sqrt{b})^2} = \sqrt{a+b+2 \sqrt{ab} }\\ \sqrt{0.3+ \sqrt{0.08} } = \sqrt{a} + \sqrt{b} \\ \sqrt{0.3 +2 \sqrt{0.02} }=\sqrt{a+b+2 \sqrt{ab} } \\ 0.3+2\sqrt{0.02}=(a+b)+2 \sqrt{ab}$
$(a+b)=0.3 \\ ab=0.02 \\ \\ \\ \frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab} \\ \\ \frac{a+b}{ab} =\frac{0.3}{0.02} \\\frac{0.3}{0.02}=15 \\ \\ \frac{1}{a} + \frac{1}{b}=15$