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Question

If 2x4=y4+z4, xyz=8 and logy x,logz y,logx z are in G.P., then find the value of x,y,z belonging to R.

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Solution

(logz y)2=(logy x)(logx z)
or (log ylog z)2=log xlog y,log zlog x
or (log y)3=(log z)3y=z.
2x4=2y4x=y=z
Also xyz=8x3=8
x=2=y=z.

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