# System of Equations

Algebra Level 4

$\begin{cases} { a }^{ 2 }+ab+{ b }^{ 2 }=25\\ { b }^{ 2 }+bc+{ c }^{ 2 }=49\\ { c }^{ 2 }+ca+{ a }^{ 2 }=64 \end{cases}$

Let $$a,b$$ and $$c$$ be positive real numbers satisfying the system of equations above. Find $$(a+b+c)^2$$.

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