若实数x,y满足2x²-6xy+9y²-4x+4=0,求根号y的值.
问题描述:
若实数x,y满足2x²-6xy+9y²-4x+4=0,求根号y的值.
答
答:
2x²-6xy+9y²-4x+4=0
(x²-4x+4)+(x²-6xy+9y²)=0
(x-2)²+(x-3y)²=0
所以:
x-2=0
x-3y=0
解得:x=2,y=2/3
所以:
√y=√(2/3)=√6/3