Question

已知实数（X^2+2X+3）（Y^2+3Y/2+1/3)=4/9,求X+Y的值

Answer 1

（X^2+2X+3）（Y^2+2Y/3+1/3)=[(x+1)^2+2] [(y+1/3)^2 +2/9]=(x+1)^2(y+1/3)^2+2/9(x+1)^2+2(y+1/3)^2+4/9=4/9

所以]=(x+1)^2(y+1/3)^2+2/9(x+1)^2+2(y+1/3)^2=0

所以x+1=0 y+1/3=0 所以 x+y=-4/3