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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