# MTMTK System

Author: alexysxeightn
Problem has been solved: 19 times

Русский язык | English Language

Numbers $a,b,c$, are such that $$\begin{cases} a^2=\frac{b^3+9\sqrt{3}}{3b}=\frac{c^3+16}{3c} \\ b^2=\frac{a^3-10}{3a}=\frac{c^3+28}{3c} \\ c^2=\frac{b^3+45\sqrt{3}}{3b}=\frac{a^3-88}{3a} \end{cases} a,b,c \in \mathbb{R}$$ What is the value of $a \cdot c$?