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Question
If `a/c = c/d = c/f` prove that : (b2 + d2 + f2) (a2 + c2 + e2) = (ab + cd + ef)2
Solution
`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e = fk
L.H.S. = (b2 + d2 + f2) (a2 + c2 + e2)
= (b2 + d2 + f2) (b2 k2 + d2 k2 + f2 k2)
= k2 (b2 + d2 + f2) k2 (b2 + d2 + f2)
= k2 (b2 + d2 + f2)2
R.H.S. = (ab + cd + ef)2
= (b. kb + dk. d + fk. f)2
= (kb2 + kd2 + kf2)
= k2 (b2 + d2 + f2)2
∴ L.H.S. = R.H.S.
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