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If x+(1)/(x)=6, find : x^2+ (1)/(x^2)...

If `x+(1)/(x)=6,` find : `x^2+ (1)/(x^2)`

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Let `(1/x)=y` So,`x=1/y`
Let `(1/x)=y` So,`x=1/y`
`x+y=6` (given)
squaring both side, we get
`(x^2+y^2+2yx)=36`
`x^2+y^2+2xxx(1/x)=36`
`x^2+ 1/x^2+2=36`
`x^2+1/x^2=34`
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