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Question
If p, q and r in continued proportion, then prove the following:
(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)
Solution
p : q :: q : r => q2 = pr1
LHS (p2 _ q2)( q2 + r2)
= (p2 -(pr)2)(pr)2 + r2)
= p3r - p2r2 + p2r2 - pr3
= pr (p2 - r2)
RHS
(q2 - r2)(p2 + q2)
= ((pr)2-r2 )(p2+ (pr)2)
= p3r - p2r2 + p2t2 - pr3
= pr(p2 - r2)
LHS = RHS. Hence, proved.
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