if x = 3+√3 then x^2 + 1/x^2 = ????
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x^2 + 1/x^2 = (x + 1/x) ^2 - 2x
= [ 3+√3 + 1/【3+√3】 ]^2 - 2× 3+√3 ×1/3+√3
= {3+√3 + (3-√3)/6 }^2 - 2
= {(18+ 6√3 +3 - √3)/6 }^2 - 2
= {(21 + 5√3)/6}^2 - 2
= (441 + 75 + 210√3 )/36 - 2
= (441 + 75 + 210√3 - 72)/36
= [444 + 210√3 ]/36
= (74+ 35√3)/6.
Hope it's helpful to u.
= [ 3+√3 + 1/【3+√3】 ]^2 - 2× 3+√3 ×1/3+√3
= {3+√3 + (3-√3)/6 }^2 - 2
= {(18+ 6√3 +3 - √3)/6 }^2 - 2
= {(21 + 5√3)/6}^2 - 2
= (441 + 75 + 210√3 )/36 - 2
= (441 + 75 + 210√3 - 72)/36
= [444 + 210√3 ]/36
= (74+ 35√3)/6.
Hope it's helpful to u.
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