Strange Equality Condition

Algebra Level 3

Let \(x,\) and \(y,\) and \(z\) be real numbers satisfying \(\dfrac{x}{y+z}+\dfrac{y}{z+x}+\dfrac{z}{x+y}=1.\)

Find the maximum value of \(\dfrac{x^2}{y+z}+\dfrac{y^2}{z+x}+\dfrac{z^2}{x+y}.\)

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