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Question
If `a/b = c/d = e/f`, prove that `(ab + cd + ef)^2 = (a^2 + c^2 + e^2) (b^2 + d^2 + f^2)`.
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Solution
Let `a/b = c/d = e/f = k` then
a = bk, c = dk and e = fk
L.H.S.
= (ab + cd + ef)2
= (bk·b + dk·d + fk·f)2
= k2 (b2 + d2 + f2)2
R.H.S.
= (a2 + c2 + e2)(b2 + d2 + f2)
= (b2k2 + d2k2 + f2k2)(b2 + d2 + f2)
= k2 (b2 + d2 + f2)(b2 + d2 + f2)
= k2 (b2 + d2 + f2)2.
L.H.S. = R.H.S.
Hence proved.
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