Question

用适当的方法解下列方程

（1）3x²-1=6x
（2）（3x-2）²=（2x-3）²
（3）y²-2y-399=0
（4）（3x-2²-5（3x-2）+4=0

Answer 1

(1) 3x^2-1=6x
3x^2-6x=1
3(x^2-2x+1)=1+3
3(x-1)^2=4
(x-1)^2=4/3
x-1=±2/3√3
x=1±2/3√3
x=(3±2√3)/3
(2) (3x-2)^2=(2x-3)^2
(3x-2)^2-(2x-3)^2=0
[(3x-2)+(2x-3)][(3x-2)-(2x-3)]=0
(5x-5)(x+1)=0
5(x-1)(x+1)=0
x-1=0
x1=1
x+1=0
x2=-1
(3) y^2-2y-399=0
(y-1)^2=399+1
y-1=±20
y=1±20
y1=1-20
y1=-19
y2=1+20
y2=21
(4) (3x-2)^2-5(3x-2)+4=0
[(3x-2)-1][(3x-2)-4]=0
(3x-3)(3x-6)=0
9(x-1)(x-2)=0
x-1=0
x1=1
x-2=0
x2=2