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Question

If a,b,c,d are in continued proportion, prove that
(a2b2)(c2d2)=(b2c2)2

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Solution

Given a,b,c,d are in continued proportion
ab=bc=cd=k(say)
c=dk,b=ck=k2d,a=bk=k3d
LHS=(a2b2)(c2d2)=(k6d2k4d2)(k2d2d2)=k4d4(k21)2=(k4d2k2d2)2=((k2d)2(kd)2)2
=(b2c2)2=RHS
Hence Proved

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