已知实数x,y满足5x²+2y²+1=6xy+4x-2y,则x²-xy+2000y²的值是?

已知实数x,y满足5x²+2y²+1=6xy+4x-2y,则x²-xy+2000y²的值是?
已知实数x,y满足5x²+2y²+1=6xy+4x-2y,则x²-xy+2000y²的值是?

已知实数x,y满足5x²+2y²+1=6xy+4x-2y,则x²-xy+2000y²的值是?
将其看出关于x的方程 5x²-(6y+4)x+2y²+2y+1=0
其判别式△≥0
而 △=(6y+4)²-20(2y²+2y+1)
=-4y²+8y-4
=-4(y-1)²
从而 y=1,代入原方程,得 x=1
从而 x²-xy+2000y²=2000