7. Solve the equation $x^{6}=y^{3}+217$ in integers.

ANSWER: $(-1,-6)(1,-6)(-3,8),(3,8)$.
Solution: Note that $y^{3}+217$ >= 0, hence, $y >= -6$.

We check that $Y=-1,-2,-3,-4,-5$ do not provide solutions, and for $y=-6$ we get $x=+/-1$.

Note that $\mathrm{y}^{3}+217=\mathrm{x}^{6}>=(\mathrm{y}+1)^{3}$, from which $\mathrm{y}^{2}+\mathrm{y}$ in mathematics

Final stage tasks for the 2015/2016 academic year for 9th grade