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Question

If x, y, z are in continued proportion then show that x-yx-z=yy+z.

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Solution

Given:xy=yzL.H.S.=x-yx-z=xy-1xy-zy Dividing by y=yz-1yz-zy xy=yz =y-zzy2-z2zy=y-zz×zyy-zy+z=yy+z=R.H.S. x-yx-z=yy+z

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