Now, just square it

Algebra Level 3

{a+b+c=abc1a+1b+1c=1\large \begin{cases} a + b + c = -abc \\ \dfrac 1a + \dfrac 1b + \dfrac 1c = 1 \end{cases}

Given the above, where a,b,c0a, b, c \ne 0, find 1a2+1b2+1c2\dfrac 1{a^2} + \dfrac 1{b^2} + \dfrac 1{c^2}.

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