Dokaži da za sve pozitivne realne brojeve xxx, yyy, zzz vrijedi nejednakost x2xy+z+y2yz+x+z2zx+y⩾(x+y+z)33[x2(y+1)+y2(z+1)+z2(x+1)].\frac{x^2}{xy + z} + \frac{y^2}{yz + x} + \frac{z^2}{zx + y} \geqslant \frac{(x + y + z)^3}{3[x^2(y + 1) + y^2(z + 1) + z^2(x + 1)]}.xy+zx2+yz+xy2+zx+yz2⩾3[x2(y+1)+y2(z+1)+z2(x+1)](x+y+z)3.