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Question

If a,b,c,d be in G.P., prove that
(bc)2+(ca)2+(db)2=(ad)2

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Solution

a,b,c,d are in G.P.
b2=ac, c2=bd and ad=bc
To prove:- (bc)2+(ca)2+(db)2=(ad)2
L.H.S =2b2+2c2+a2+d22bc2ac2bd
Using above results
L.H.S =2b2+2c2+a2+d22ad2b22c2
L.H.S =a2+d22ad=(ad)2= R.H.S
Hence proved.

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