Question

Ifx=2^1/3+3^1/2then x^3+1/x^3=

Answer 1

Answer:

If x+1/x=2, then what is the value of x^3+1/x^3?

Let p (x) = x + 1 / x = 2

= x + 1 = 2x

= 2x - x = 1

or, x = 1.

let g(x) = x^3 + 1/x^3

since, x = 1

therefore,

g (1) = (1)^3 +1 / (1)^3

= 1 + 1 / 1

= 2 / 1

= 2

So, the answer to your question is 2.

You can also make it this way -

x + 1/ x = 2

Cubing both sides, we get -

x^3 + 1/x^3 + 3×x×1/x (x + 1/x) = 8

= x^3 + 1/x^3 + 3 (x + 1/x) = 8

= x^3 + 1/x^3 + 3 × 2 = 8 (since, x + 1/ x = 2)

= x^3 + 1/x^3 = 8 - 6

or, x^3 + 1/x^3 = 2.

Hope this answer helps you out.