If x2 + 1/x2=7 then find value of x3 + 1/x3 - Maths - Polynomials

Question

If x2 + 1/x2=7 then find value of
x3 + 1/x3

Rdblaze · Accepted Answer

(x + 1/x)2 = x2 + 1/x2 + 2
(x + 1/x)2 = 9
x + 1/x = 3
now
(x + 1/x)3 = x3 + 1/x3 + 3(x +
1/x)
27 = x3 + 1/x3 + 9
or
x3 + 1/x3 = 27 - 9 = 18
it shoul be the answer