if x=2+root3, find x+1/x and x2-1/x2

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x=2+√3
1/x=1/2+√3
=(1/2+√3)×2-√3/2-√3
=2-√3
x+1/x=(2+√3)+(2-√3)
=4
And 2x-1/x^2 =2(2+√3)-1/(2+√3)^2
=4+2√3-1/7+4√3
=4+2√3-7+4√3
=-3+6√3
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