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Question

If the mean of x and 1/x is M then the mean of x3 and 1/x3 is

A
M(M23)2
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B
M(4M23)
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C
M3
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D
M3+3
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Solution

The correct option is B M(4M23)
x+1x2=M [ Given ]
x+1x=2M ----- ( 1 )

(x+1x)3=(2M)3

x3+1x3+3×x×1x×(x+1x)=8M3

x3+1x3+3(x+1x)=8M3

x3+1x3+3(2M)=8M3 [ From ( 1 ) ]

x3+1x3+6M=8M3

x3+1x3=8M36M

x3+1x32=8M36M2

x3+1x32=4M33M

x3+1x32=M(4M23)

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