5 x²+2y²+2xy-14x-10y+17=0求x,y

题目

5 x²+2y²+2xy-14x-10y+17=0求x,y
请用初中知识
5 x²+2y²+2xy-14x-10y+17=0求x、y

答案

5 x^2+2y^2+2xy-14x-10y+17
=(x^2+y^2+2xy-6x-6y+9)+(4x^2-8x+4)+(y2-4y+4)
=(x+y-3)^2+4(x-1)^2+(y-2)^2=0
所以x+y-3=0
x-1=0
y-2=0
所以x=1,y=2