Question

If
`\sqrt{0.3+ √(0.08) } = √(a) + √(b)` Then 1/a + 1/b = ....

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Answer 1

`\sqrt{0.3+ √(0.08) } = √(a) + √(b) \\ \\ \sqrt{0.3+ √(0.08) } \\ = \sqrt{0.3+ √(4*0,02) } \\ = \sqrt{0.3 +2 √(0.02) } \\ \\ (a+b)^2=a^2+b^2+2ab\\ \\ \sqrt{ (√(a) + √(b))^2} = \sqrt{a+b+2 √(ab) }\\ \sqrt{0.3+ √(0.08) } = √(a) + √(b) \\ \sqrt{0.3 +2 √(0.02) }=\sqrt{a+b+2 √(ab) } \\ 0.3+2√(0.02)=(a+b)+2 √(ab) \\`

`(a+b)=0.3 \\ ab=0.02 \\ \\ \\ (1)/(a) + (1)/(b) = (a+b)/(ab) \\ \\ (a+b)/(ab) =(0.3)/(0.02) \\(0.3)/(0.02)=15 \\ \\ (1)/(a) + (1)/(b)=15`