If $$x + \frac{1}{x} = 10,  then  x^3 + \frac{1}{x^3}$$ is equal to:

Given,

$$x + \frac{1}{x} = 10$$

We have to find,

$$x^3 + \frac{1}{x^3}$$

First we have to know what is $$a^3 + b^3$$ i.e $$(a+b)(a^2 -ab + b^2)$$

Putting the same for x an 1/x, we get

$$\left({x + \frac{1}{x}}\right)\left(x^2 -1 + \frac{1}{x}^2\right)$$...(i)

and Again we have to find $$(x^2 + \frac{1}{x}^2)$$ , From the formula of $$a^2 +b^2$$ = $$(a + b)^2 -2ab$$,

we got $$(x^2 + \frac{1}{x}^2$$) = $$(x + \frac{1}{x})^2 -2)$$ = 98.

Hence we have now ,

10*(98-1=97)=970