Question

if x+1/x is 7 . then find x^3+1/x^3

Answer 1

Given x + 1/x = 7.

On cubing both sides, we get

(x + 1/x)^3 = (7)^3

We know that (a + b)^3 = a^3 + b^3 + 3ab(a + b).

Here a = x, b = 1/x.


x^3 + 1/x^3 + 3 * x * (1/x)(x + 1/x) = 343

x^3 + 1/x^3 + 3(x + 1/x) = 343

x^3 + 1/x^3 + 3(7) = 343

x^3 + 1/x^3 = 21 = 343

x^3 + 1/x^3 = 343 - 21

x^3 + 1/x^3 = 322.


Hope this helps!