Question

x,y∈R,比较4x^2+2y^2+6与8x一8y一6的大小

Answer 1

(4x^2+2y^2+6)-(8x一8y一6)

=4x^2+2y^2-8x+8y+12

=4(x^2-2x+1)+2(y^2+4y+4)

=4(x-1)^2+2(y+2)^2

≥0

所以,

4x^2+2y^2+6≥8x-8y-6

(下面的讨论可以不用)

①x=1,且y=-2时,

4x^2+2y^2+6=8x-8y-6

② x≠1,或y≠-2时, 4x^2+2y^2+6＞8x-8y-6