Question

证明,若abc属于R,且x=a^2-2*b+1,y=b^2-2*c+1,z=c^2-2*a+1,则x,y,z中至少有一个

Answer 1

若abc属于R,且x=a^2-2*b+1,y=b^2-2*c+1,z=c^2-2*a+1,则

x+y+z

=a^2-2*b+1+b^2-2*c+1+c^2-2*a+1

=(a-1)^2+(b-1)^2+(c-1)^2

≥0

所以x,y,z中至少有一个不小于0