Question

用配方法解下列方程

Answer 1

x^-2x-3=0
x^-2x+1-4=0
(x-1)^2=4
x-1=±2
x=3或x=-1

2x^2-7x+6=0
2[x^2-7x/2+(7/4)^2]-2*49/16+6=0
2(x-7/4)^2=2/16
(x-7/4)^2=1/16
x-7/4=±1/4
x=2或者3/2
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Answer 2

1、
x^2-2x-3=0
===> x^2-2x+1=3+1=4
===> (x-1)^2=4
===> x-1=2，或者x-1=-2
===> x=3，或者x=-1

2、
2x^2-7x+6=0
===> 2[x^2-(7/2)x+(49/16)]-2*(49/16)+6=0
===> 2*[x-(7/4)]^2=(49/8)-6=1/8
===> [x-(7/4)]^2=1/16
===> x-(7/4)=1/4，或者x-(7/4)=-1/4
===> x=2，或者x=3/2

Answer 3

x^2-2x-3=x^2-2x+1-4=(x-1)^2-4=0
所以(x-1)^2=4,x-1=±2，x=3或x=-1

2x^2-7x+6=0，两边同除以2，x^2-7x/2+3=0
即(x-7/4)^2+3-(7/4)^2=(x-7/4)^2-1/16=0
所以(x-7/4)^2=1/16,
x-7/4=±1/4
x=2或者3/2