Question

试说明:不管a,b取何值,2a^2+5b^2-2ab+2a-4b+5的值始终为正数.

Answer 1

2a^2+5b^2-2ab+2a-4b+5

=2a^2+5b^2+(a-b)^2-a^2-b^2+2a-4b+5

=a^2+2a+1+4b^2-4b+1+(a-b)^2+3

=(a+1)^2+(2b-1)^2+(a-b)^2+3

无论ab取何值,结果都大于3,为正数!