If `x=3-2sqrt(2)`,find `x^2+1/(x^2)`

Explanation

Given `x=3-2sqrt2`
Find :- `x^2+1/x^2`
`1/x=1/(3-2sqrt2)xx(3+2sqrt2)/(3+2sqrt2)`
`1/x=(3+2sqrt2)/(3^2-(2sqrt2)^2)`
`1/x=(3+2sqrt2)/(9-8)`
`1/x=3+2sqrt2`
Now,
`x+1/x=3-2sqrt2+3+2sqrt2`
`x+1/x=6`
Again squaring both side
`(x+1/x)^2=(6)^2`
`x^2+1/(x^2)+2xx x xx1/x=36`
`x^2+1/(x^2)+2=36`
`x^2+1/(x^2)=36-2`
`x^2+1/(x^2)=34`