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Question

If logxy,logzx,logyz are in G.P., xyz=64 and x3,y3,z3 are in A.P., find x+y+z

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Solution

According to question,
logzxlogxy=logyzlogzx(logx)3=(logz)3
x=z
Since 2y3=x3+z3x2=y3 or x=y
Given xyz=64 & x=y=z
x=y=z=4
& x+y+z=12

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