设4X²+y²+4X-8Y+17=0 求X+y的值
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设4X²+y²+4X-8Y+17=0 求X+y的值
设4X²+y²+4X-8Y+17=0 求X+y的值
设4X²+y²+4X-8Y+17=0 求X+y的值
4X²+y²+4X-8Y+17=0
﹙4x²+4x+1﹚+﹙y²-8y+16﹚=0
﹙2x+1﹚²+﹙y-4﹚²=0
∵ ﹙2x+1﹚²≥0,﹙y-4﹚²≥0
∴ 2x+1=0,x=﹣1/2
y-4=0,y=4
∴ x+y=﹣1/2+4=7/2.
4X²+y²+4X-8Y+17=0
整理为
(2x+1)^2+ (y-4)^2=0
平方非负
故2x+1=0 , x=-0.5
y-4=0, y=4
因此,x+y=3.5