MTMTK System
Author: alexysxeightn
Problem has been solved: 21 times
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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 $a \cdot c$?
Числа $a,b,c$, удовлетворяющих системе
$$
\begin{cases}
a^2=\frac{b^3+9\sqrt{3}}{3b}=\frac{c^3+16}{3c} \\
b^2=\frac{a^3-10}{3a}=\frac{c^3+28}{3c} \\
c^2=\frac{b^3+45\sqrt{3}}{3b}=\frac{a^3-88}{3a}
\end{cases} a,b,c \in \mathbb{R}$$
Чему рано $a \cdot c$?
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