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Question
If `a/b = c/d = e/f`, prove that each ratio is `[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`
Solution
`a/b = c/d = e/f` = k(say)
∴ a = k, c = dk, e = fk
`[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`
= `[(2b^3k^3 + 5d^3k^3 + 7f^3k^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`
= `k[(2b^3 + 5d^3 + 7f^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)` = k
Hence proved.
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