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The minimum value of ((x+1/x)^6-(x^6+1/...

The minimum value of `((x+1/x)^6-(x^6+1/(x^6))- 2)/((x+1/x)^3+x^3+1/x^3)` is (for x>o)

Text Solution

Verified by Experts

The correct Answer is:
6
`:'N^(r)=(x+1/x)^(6)-(x^(6)+1/(x^(6)))-2`
`=(x+1/x)^(6)=(x^(3)+1/(x^(3)))^(2)=((x+1/x)^(3)+(x^(3)+1/(x^(3))))`
`((x+1/x)^(3)-(x^(3)+1/(x^(3))))`
`=D^(r).(3(x+1/x))`
`:.(N^(r))/(D^(r))=3(x+1/x)ge6`
Hence minimum value of `(N^(r))/(D^(r))` is 6.
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