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If a/b = b/c and a, b, c > 0, then show that (a2 + b2) (b2 + c2) = (ab +bc)2 |
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Answer» (a2 + b 2)(b2 + c2 ) = (ab + bc)2 b = ck; a = ck2 L.H.S = (a2 + b2 ) (b2 + c2 ) = [(ck2 ) + (ck2) ] [(ck)2 + c2 ] … [From (i) and (ii)] = [c2 k2 + c2 k2 ] [c2 k2 + c2 ] = c2 k2 (k2 + 1) c2 (k2 + 1) = c4k2 (k2 + 1)2 R.H.S = (ab + bc)2 = [(ck2 ) (ck) + (ck)c]2 …[From (i) and (ii)] = [c2 k2 + c2 k]2 = [c2 k (k2 + 1)]2= c4 (k + 1)2 ∴ L.H.S = R.H.S ∴ (a2 + b2 ) (b2 + c2 ) = (ab + bc)2 |
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