Question

If (x+1/x)^2=3, find x^3+1/x^3​

Answer 1

Answer:

Given

(x +1/x)^2 = 3

or, x+1/x = √3

Using Identity , (a+b)^3 = a^3 +b^3 + 3ab(a+b)

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

or, (x +1/x)^3 = x^3 + 1/x^3 + 3(√3)

or, (√3)^3 = x^3 + 1/x^3 + 3√3

or, 3√3 = x^3 + 1/x^3 + 3√3

or, x^3 + 1/x^3 = 0