MathDB

x

y

and

z

are real numbers where the sum of any two among them is not

1

. Show that,

\dfrac{(x^2+y)(x+y^2)}{(x+y-1)^2}+\dfrac{(y^2+z)(y+z^2)}{(y+z-1)^2} + \dfrac{(z^2+x)(z+x^2)}{(z+x-1)^2} \ge 2(x+y+z) - \dfrac{3}{4}

Find all triples

(x,y,z)

of real numbers satisfying the equality case.

2