Question

if x=2+root 3 find the value of x³+1/x³​

Answer 1

Answer:

so, 1/x= 1/2+√3

= 1/2+√3 ×2-√3/2-√3

= 2-√3/(2) ^2 - (√3) ^2

=2-√3/4-3

=2-√3/1

=2-√3

so, x+1/x = 2+√3+2-√3

= 4

(x+1/x) ^3 = (4) ^3 {cube both sides}

(x^3 + 1/x^3 +3×x×1/x(x+1/x) =64

x^3 +1/x^3 +3(4) =64

x^3 +1/x^3=64-12

x^3 +1/x^3 = 52 is the correct answer