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