TR-MO 2015 Problem 2 xxx , yyy and zzz are real numbers where the sum of any two among them is not 111 . Show that, (x2+y)(x+y2)(x+y−1)2+(y2+z)(y+z2)(y+z−1)2+(z2+x)(z+x2)(z+x−1)2≥2(x+y+z)−34\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}(x+y−1)2(x2+y)(x+y2)+(y+z−1)2(y2+z)(y+z2)+(z+x−1)2(z2+x)(z+x2)≥2(x+y+z)−43Find all triples (x,y,z)(x,y,z)(x,y,z) of real numbers satisfying the equality case. Dataset text AI-MO AoPS. Quoted with source. Solutions No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label. Add a solution Similar problems These problems have the most words in common with this statement. INMO 1997 Problem 2INMO 1997 Problem 3INMO 1995 Problem 5CMO 1989 Problem 2INMO 1991 Problem 4 PreviousProblem 1 NextProblem 3 Locator tr-mo/2015/p2 · Tag ATJ5ZBQ4PY · Edit this page on GitHub · Keys: j next, k previous