Question

If x^2+1/x^2=7,then find value of x^3+1/x^3

Answer 1

x^2 +  1/x^2 = 7
(x + 1/x)^2 = 5

(x + 1/x) = √5

x³ + 1/x³  =  (x + 1/x)^3 - 3 x/x * (x + 1/x) = 5√5 - 3 * √5 = 2 √5