# Cool inequality #0 Making it easy

Algebra Level 5

If $$a, b,$$ and $$c$$ are real numbers such that $$a^2 + b^2 + c^2 = 1$$, then the value of $$ab+bc+ca$$ is on the interval $$[A, B]$$ where $$A$$ is as large as possible and $$B$$ is as small as possible.

Find $$|A| + |B|$$.

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