An algebra problem by Abhay Kumar

Algebra Level 3

If \(x,y\) and \(z\) are non-zero real numbers such that \(x^2=y+z\), \(y^2=x+z\), \(z^2=x+y\), then find the value of \(\dfrac{1}{x+1}+\dfrac{1}{y+1}+\dfrac{1}{z+1}\).

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