Question

if x=2+under root 3, find the value of x(cube) + 1/x(cube)

Answer 1

1/x = 1/(2+√3) = (4-3)/ (2+√3)

= (2-√3)(2+√3)/(2+√3)

= 2-√3

x^3 + 1/x^3

= ( x+ 1/x)^3 - 3×x× 1/x( x+ 1/x)

= 2+√3 +2-√3)^3 - 3( 2+√3 +2-√3)

= 4^3 - 3(4)

= 64 -12 = 52