## SUBJECT II

Solve the equation $2 \sqrt[3]{2 x-1}=x^{3}+1$.
Solution:
Let $\sqrt[3]{2 x-1}=t$ and we have that $t^{3}=2 x-1$ ..... $1 p$
$2 t=x^{3}+1 \Leftrightarrow x^{3}=2 t-1$ ..... $1 p$
$t^{3}-x^{3}=2 x-2 t$ ..... $1 p$
$x_{1}=1, x_{2,3}=\frac{-1 \pm \sqrt{5}}{2}$ ..... $.4 p$

## MATHEMATICS OLYMPIAD  LOCAL STAGE - 21.02.2016  GRADING SCALE  GRADE 10