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Question
If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`
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Solution
Given, a, b and c are in continued proportion.
Therefore,
`a/b = b/c`
ac = b2
Here,
`(a^2 + ab + b^2)/(b^2 + bc + c^2) = (a^2 + ab + ac)/(ac + bc + c^2)`
= `(a(a + b + c))/(c(a + b + c))`
= `a/c`
Hence proved.
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