|
|
Lấy a=min{a,b,c}, b=a+u và c=a+v,u,v≥0.
Ta có , P−233=14(a2+b2+c2)(a+b+c)2+(ab+bc+ca)(a+b+c)a2b+b2c+c2a−233=
=13(a+b+c)2(a2b+b2c+c2a)(57(u2−uv+v2)a3+
+3(22u3−18u2v+9uv2+22v3)a2+(25u4−11u3v−18u2v2+43uv3+25v4)a+
+(22u3−37u2v+28uv2+2v3)uv)≥0
Vậy minP=233 ⇔a=b=c=13.
|