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Question

If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P. Show that : x2, b2, y2 are in A.P.

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Solution

If a,b,c are in AP it follows that

a plus c equals 2 b ……..(1)

and a,x,b and b,y,c are in individual GPs which follows

x squared equals a b …….(2)

y squared equals b c ……..(3)

Adding eqn 2 and 3 we get,

x squared plus y squared equals a b plus b c

x squared plus y squared space equals b left parenthesis a plus c right parenthesis x squared plus y squared space equals b asterisk times 2 b left parenthesis f r o m e q n 1 right parenthesis x squared plus y squared space equals 2 b squared

which shows x squared comma space b squared comma space y squared space are in AP.


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