Question

Please answer fast as possible ​

Answer 1

Given:

x = 2 + √3

To Find:

x³ + 1/x³

Solution:

x = 2 + √3

(1/x) = (1/2 + √3) * (2 - √3/2 - √3)

      = (2 - √3)

So,

x + 1/x = (2 + √3) + (2 - √3)

          = 4

Cube on both the sides.

(x + 1/x)³ = 4³

==> x³ + 1/x³ + 3(x * 1/x)(x + 1/x) = 64

==> x³ + 1/x³ + 3(1)(4) = 64

==> x³ + 1/x³ + 12 = 64

==> x³ + 1/x³ = 52

Result:

x³ + 1/x³ = 52

Answer 2

Answer:

52

Step-by-step explanation:

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