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Question
If `a/b = c/d = e/f`, prove that: (a2 + c2 + e2) (b2 + d2 + f2) = (ab + cd + ef)2
Theorem
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Solution
`a/b = c/d = e/f` = k
a = bk, c = dk, e = fk
L.H.S.
= (a2 + c2 + e2) (b2 + d2 + f2)
= ((bk)2 + (dk)2 + (fk)2) (b2 + d2 + f2)
= (b2k2 + d2k2 + f2k2) (b2 + d2 + f2)
= k2(b2 + d2 + f2) (b2 + d2 + f2)
= k2(b2 + d2 + f2)2
R.H.S.
= (ab + cd + ef)2
= ((bk)b + (dk)d + (fk)f)2
= (b2k + d2k + f2k)2
= (k(b2 + d2 + f2))2
= k2(b2 + d2 + f2)2
L.H.S. = R.H.S.
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Chapter 7: Ratio and proportion - Exercise 7B [Page 126]
