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Question

If x, y, z are in continued proportion, prove that : (x+y)2(y+z)2=xz

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Solution

x,y,z are in continued proportion, that is
xy=yz .......... (1)
then,y2=xz
Now,(x+y)2(y+z)2 =y2(xy+1)2z2(yz+1)2
=y2(xy+1)2z2(xy+1)2 ( from (1) xy=yz )
=y2z2
=xzz2
=xz

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