Question

CMR: a^2+b^2+1 >= ab+a+b
 

Answer 1

Ta có a^2+b^2+1>=ab+a+b (1)

<=> 2a^2+2b^2+2>=2ab+2a+ab

<=>2a^2+2b^2+2-2ab-2a-2b>=0

<=>(a^2-2ab+b^2)+(a^2-2a+1)+(b^2-2b+1)>=0

<=>(a-b)^2+(a-1)^2+(b-1)^2>=0 luôn đúng

       Vây BĐT(1) đúng (đpcm)

Answer 2

a²+b²+1-ab-a-b>=0

2a²+2b²+2-2ab-2a-2b>=0

(a-b)²+(a-1)²+(b-1)²>=0

Dấu = xảy ra khi a=b

Answer 3

Thanks