Strange Equality Condition

Algebra Level 4

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

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