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Question
If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.
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Solution
Since a, b, c are in continued proportion,
`a/b = b/c`
`=>` b2 = ac
Now, (a2 + b2)(b2 + c2) = (a2 + ac)(ac + c2)
= a(a + c) c(a + c)
= ac(a + c)2
= b2(a + c)2
`=>` (a2 + b2)(b2 + c2) = [b(a + c)][b(a + c)]
`=> (a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`
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