parmenides51 wrote: If $x^3-3\sqrt3 x^2 +9x - 3\sqrt3 -64=0$ find the value of $x^6-8x^5+13x^4-5x^3+49x^2-137x+2015$ . First equation is $(x-\sqrt 3)^3=64$ and so, assuming we are speaking of real numbers, $x=4+\sqrt 3$ Plugging in the second, we get $\boxed{1898}$

@pco Is there any special way to get 1898 or just doing calculations?

@above note that $x^6-8x^5+13x^4=0$ at $x=4+\sqrt3$