Пусть a,b,c,d>0a, b, c, d > 0a,b,c,d>0, abcd=1abcd=1abcd=1. Докажите неравенство (a−1)(c+1)1+bc+c+(b−1)(d+1)1+cd+d+(c−1)(a+1)1+da+a+(d−1)(b+1)1+ab+b≥0.{(a-1)(c+1)\over 1+bc+c}+{(b-1)(d+1)\over 1+cd+d}+{(c-1)(a+1)\over 1+da+a} +{(d-1)(b+1)\over 1+ab+b}\geq 0.1+bc+c(a−1)(c+1)+1+cd+d(b−1)(d+1)+1+da+a(c−1)(a+1)+1+ab+b(d−1)(b+1)≥0.