已知实数x和y满足5x方-3xy+1/2y方-2x+1/2y+1/4=0 求x与y的值

题目

已知实数x和y满足5x方-3xy+1/2y方-2x+1/2y+1/4=0 求x与y的值

答案

5x²-3xy+1/2y²-2x+1/2y+1/4=0
两边乘以2得：
10x²-6xy+y²-4x+y+1/2=0
配方得：
（3x-y-1/2)²+（x-1/2)²=0
∴必有3x-y-1/2=0
x-1/2=0
解得 x=1/2,y=1.