Question

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

Answer 1

x = 2 + √3

1/x = 1/(2 + √3)

= (2 -√3)/(2 +√3)(2 -√3)

= (2 -√3)/(2² -√3²)

= (2 - √3)

hence, x + 1/x = (2+√3)+(2-√3) = 4

x³ + 1/x³ = (x + 1/x)³ -3(x + 1/x)

= (4)³ - 3(4)

= 64 -12

= 52

Answer 2

x = 2+√3

1/x = 1/(2 + √3)

= (2 -√3)/(2 +√3)(2 -√3)

= (2-√3)/(2² -√3²)

= (2-√3)

x+1/x = 2+√3+2-√3

= 4

(x+1/x)³ = x³+1/x³+3(x)(1/x)[x+1/x]

x³+1/x³ = (4)³-3(4)

= 64-12

= 52

Hope it helps