用配方法解下列方程,
问题描述:
用配方法解下列方程,
(1) x²-6x=-8 (2)x²-8x-4=0
(3) x²+3x+2=0 (4) -x²+5x+6=0
答
(1) x²-6x=-8
x²-6x+8=0
x²-6x+9-1=0
(x-3)^2-1=0
(x-3)^2=1
x-3=±1
x=4或2
(2)x²-8x-4=0
x²-8x+16-20=0
(x-4)^2=20
x=4±2根号5
(3)x²+3x+2=0
x²+3x+9/4-1/4=0
(x+3/2)^2=1/4
x=±1/2-3/2
x=-1或-2
(4)-x²+5x+6=0
-(x²+5x)+6=0
-(x²+5x+25/4)+49/4=0
-(x+5/2)^2=-49/4
x=±7/2-5/2
x=1或-6
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