Question

If x=2+√3, Find x^(3)+1/x^3
PLEASE ANSWER

Answer 1

Answer:

52

Step-by-step explanation:

Given: x = 2 + √3.

Then,

(1/x) = (1/2 + √3) * (2 - √3/2 - √3)

      = (2 - √3)/(2)² - (√3)²

      = (2 - √3)/1

      = 2 - √3

Now,

⇒ x + (1/x) = 2 + √3 + (2 - √3)

⇒ x + (1/x)  = 4

On cubing both sides, we get

⇒ (x + 1/x)³ = 4³

⇒ x³ + 1/x³ + 3(x + 1/x) = 64

⇒ x³ + 1/x³ + 3(4) = 64

⇒ x³ + 1/x³ + 12 = 64

⇒ x³ + 1/x³ = 52

Hope it helps!

Answer 2

Answer:

52

Step-by-step explanation:

x = 2 + √3

(1/x) = (1/2 + √3)

(1/2 + √3) * [2 - √3/2 - √3]

[2 - √3]/(2)^2 - (√3)^2

[2 - √3]/(4 - 3)

[2 - √3]

So,

x + 1/x

= 2 + √3 + 2 - √3

= 4

Cubing both sides, we get

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

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

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

x^3 + 1/x^3 = 52

Hope it help you