Question

x+1/x=3 find x^5+1/x^5
correct answer will be marked as brainliest

Answer 1

Given Equation is x + 1/x = 3.

On squaring both sides, we get

⇒ (x + 1/x)^2 = (3)^2

⇒ x^2 + 1/x^2 + 2 = 9

⇒ x^2 + 1/x^2 = 7

We know that x^3 + 1/x^3 = (x + 1/x)^3 - 3(x + 1/x)

⇒ (3)^3 - 3(3)

⇒ 27 - 9

⇒ 18.

Now,

⇒ (x^2 + 1/x^2)(x^3 + 1/x^3) = x^5 + 1/x^5 + x + 1/x

⇒ (7)(18) = x^5 + 1/x^5 + 3          

⇒ 126 = x^5 + 1/x^5 + 3

⇒ x^5 + 1/x^5 = 123.

Hope this helps!