# What if the variables were not integers?

Calculus Level 4

$\begin{cases} a + 3 b + 2 ab = 12.965 \\ 5 b + 2 c + 9 bc = 111.375 \\ 4 c + 4 a + 10 ac = 73.37 \end{cases}$

The above nonlinear system of equations in $$a$$, $$b$$, and $$c$$ has a unique solution with $$a \gt 0$$, $$b \gt 0$$, and $$c \gt 0$$. Find this solution numerically, and as your answer enter the value of $$10(a + b + c)$$.

Hint: You can use the multivariate Newton-Raphson method. It is very fast and efficient..

×