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Question
If `a/b = b/c` and a, b, c > 0 then show that, `[a^2 + b^2]/(ab) = (a+c)/b`
Solution
`a/b = b/c ⇒ b^2 = ac` ...(1)
LHS = `[a^2 + b^2]/(ab)`
= `[a^2 + ac]/(ab)` ...[Using 1]
= `[a( a + c )]/(ab)`
= `[a + c]/b`
RHS = `(a + c)/b`
∴ LHS = RHS
∴ `[a^2 + b^2]/(ab) = (a+c)/b`
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