若实数a,b,c,满足A=a^2-2b+π/2,B=b^2-2c+π/3,C=c^2-2a+π/6

x+y+z=a^2-2b+π/3+b^2-2c+π/6+c^2-2a+π/2
=a^2-2a+b^2-2b+c^2-2c+π
=(a-1)^2+(b-1)^2+(c-1)^2+π-3
因为π>3
所以x、y、z中至少有一个数大于0