Problem 5. Solve the equation: $\left(x^{4}+9 x^{2}+4\right)\left(y^{4}-3 y^{2}+17\right)=59$.
Answer: $\left(0 ; \pm \sqrt{\frac{3}{2}}\right)$.

Solution. Note that $x^{4}+9 x^{2}+4 \geqslant 4$ for each $x$, and $y^{4}-3 y^{2}+17=\left(y^{2}-3 / 2\right)^{2}+59 / 4 \geqslant 59 / 4$ for each $y$. Therefore, the left side of the equation is greater than or equal to $4 \cdot 59 / 4=59$, and equality is achieved only when $x=0$ and $y^{2}=3 / 2$. This gives the answer.