Now, just square it

Algebra Level 3

$\large \begin{cases} a + b + c = -abc \\ \dfrac 1a + \dfrac 1b + \dfrac 1c = 1 \end{cases}$

Given the above, where $a, b, c \ne 0$ , find $\dfrac 1{a^2} + \dfrac 1{b^2} + \dfrac 1{c^2}$ .