Question

试说明不论x、y取什么有理数,多项式x2+y2-2x+2y+3的值总是正数

Answer 1

x2+y2-2x+2y+3=(x-1)^2+(y+1)^2+1>=1

Answer 2

证明：对于任意x,y属于有理数（乃至实数），有x2+y2-2x+2y+3= x2-2x+1+y2+2y+1+1= (x-1)2+(y+1)2+1

Answer 3

证明：对于任意x,y属于有理数（乃至实数），有x2+y2-2x+2y+3= x2-2x+1+y2+2y+1+1= (x-1)2+(y+1)2+1。希望有所帮助。