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Diano4ka-milaya [45]
4 years ago
10

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 = ....
I Hope Someone Answer My question
Mathematics
1 answer:
babymother [125]4 years ago
6 0
\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


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