# Squared Inequality

Algebra Level 3

$$a,b,c$$ are reals satisfying $$ab^2+bc^2+ca^2=3$$. If the statement $\dfrac{a^2+b^2}{c^2}+\dfrac{b^2+c^2}{a^2}+\dfrac{c^2+a^2}{b^2}\ge k$ is always true for some real number $$k$$, then find the largest possible value of $$k$$.

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