Question

已知,5X^2+4X-2XY+Y^2+1=0,求(X+Y)^2的算术平方根

已知,5X^2+4X-2XY+Y^2+1=0,求(X+Y)^2的算术平方根

Answer 1

,5X²+4X-2XY+Y²+1=0,
4x²+4x+1 + x²-2xy+y²=0
（2x+1）² + （x-y）² =0
2x+1=0； x-y=0
x=-1/2，y=-1/2
∴(X+Y)²=（-1/2-1/2）²=（-1）²=1
1算术平方根是1

Answer 2

5X^2+4X-2XY+Y^2+1=0
4X^2+4X+1+X^2-2XY+Y^2=0
(2X+1)^2+(x-Y)^2=0
(2X+1)^2=0,(x-Y)^2=0
x=y=-1/2,

(X+Y)^2
=(-1/2-1/2)^2的算术平方根为：1/2