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1/x =2/3+√5
= 2/3+√5 x 3-√5/3-√5
= 2 x(3-√5)/(3)²-(√5)²
= 2(3-√5)/ 9-5
= 2(3-√5)/4
= 3-√5/2
x + 1/x = [3+√5+3-√5]/2
= 6/2
=3
x+1/x =3
(x+1/x)²=3²
= x² + 1/x² + 2 =9
= x² + 1/x² = 7
so x³+1/x³ = (x+1/x)(x² -x.1/x + (1/x)²)
x³ + 1/x³ = 3(x²+1/x² -1)
= 3(7-1)
= 3 x 6
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