A=a+b1+c2+b+c1+a2+c+a1+b2≥92(a+b+c)A=a+bab+bc+ca+c2+b+cab+bc+ca+a2+c+aab+bc+ca+b2A=a+b(c+a)(b+c)+c+b(c+a)(b+a)+a+c(c+b)(b+a)≥92(a+b+c)
+b=x;b+c=y;c+a=zA=xyz+yxz+zxy≥9x+y+z⇔(x2+y2+z2)(x+y+z)≥9xyz.{x2+y2+z2≥3x2y2z2−−−−−−√3.x+y+z≥3xyz−−−√3.⇒(x2+y2+z2)(x+y+z)≥9xyz.