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Question
If `a/c = c/d = c/f` prove that : `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"`
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Solution
`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e =fk
L.H.S. = `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2)`
= `(b^2k^2)/(b^2) + (d^2k^2)/(d^2) + (f^2k^2)/(f^2)`
= k2 + k2 + k2
= 3k2
R.H.S. = `"ac"/"bd" + "ce"/"df" + "ae"/"bf"`
= `"bk.dk"/"b.d" + "dk.fk"/"d.f" + "bk.fk"/"b.f"`
= k2 + k2 + k2
= 3k2
∴ L.H.S. = R.H.S.
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