用配方法解x²+5x-1=0,2x²-4x-1=0,1/4x²-6x+3=0

问题描述:

用配方法解x²+5x-1=0,2x²-4x-1=0,1/4x²-6x+3=0

x²+5x-1=0
(x+5/2)²-1-25/4=0
(x+5/2)²=29/4
x+5/2=±√29/2
x=(-5±√29)/2
2x²-4x-1=0
2(x²-2x)-1=0
2(x-1)²-1-2=0
(x-1)²=3/2
x-1=±√6/2
x=1±√6/2
1/4x²-6x+3=0
(1/4)(x²-24x)+3=0
(1/4)(x-12)²+3-36=0
(x-12)²=132
x-12=±2√33
x=12±2√33
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