Given x3,y3,z3 are in A.P. and logxy,logzx,logyz are in G.P. If xyz=64, then prove that x=y=z=4.
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Solution
2y3=x3+z3 or (xy)3+(zy)3=2 ......(1) (logzx)2=logxy.logyz or (logxlogz)2=logylogx,logzlogy=logzlogx ∴(logx)3=(logz)3 or logx=logz ∴x=z Hence from (1),2y3=2z3∴y=z=x But xyz=64∴x3=64 ∴x=y=z=4