Question

用因式分解法解下列一元二次方程

1. X（2X＋1）＝3（2X+1) 2. (X-2)^2=2-X 3. X(2X-1)=3(1-2X) 4. X^2-3X-10=0 5.(X-3)(X+7)= -9 6. (3Y-2)^2=(2Y-3)^2 7.(2Y+1)^2-8(2Y+1)+15=0 8. (X-1)^2=2X(1-X)
要详细过程哦！谢谢

Answer 1

1. X（2X＋1）＝3（2X+1)
X（2X＋1）-3（2X+1)=0
(2X+1)(X-3)=0
X=-1/2,X=3

2. (X-2)^2=2-X
(X-2)^2+(X-2)=0
(X-2)(X+1)=0
X=2,X=-1

3. X(2X-1)=3(1-2X)
X(2X-1)+3(2X-1)=0
(2X-1)(X+3)=0
X=1/2,X=-3

4. X^2-3X-10=0
X^2-5X+2X-10=0
X(X-5)+2(X-5)=0
(X-5)(X+2)=0
X=5,X=-2

5.(X-3)(X+7)= -9
X^2+4X-21+9=0
X^2+4X-12=0
X^2+6X-2X-12=0
X(X+6)-2(X+6)=0
(X+6)(X-2)=0
X=-6,X=2

6. (3Y-2)^2=(2Y-3)^2
(3Y-2)^2-(2Y-3)^2=0
[(3Y-2)+(2Y-3)][(3Y-2)-(2Y-3)]=0
(5Y-5)(Y+1)=0
Y=1,Y=-1

7.(2Y+1)^2-8(2Y+1)+15=0
(2Y+1-3)(2Y+1-5)=0
4(Y-1)(Y-2)=0
Y=1,Y=2

8. (X-1)^2=2X(1-X)
(X-1)^2+2X(X-1)=0
(X-1)(X-1+2X)=0
(X-1)(3X-1)=0
X=1,X=1/3

Answer 2

1. X（2X＋1）＝3（2X+1)
(2x+1)(x-3)=0
x=-1/2,或x=3

2. (X-2)^2=2-X
(x-2)(x-1)=0
x=2或x=1

3. X(2X-1)=3(1-2X)
(2x-1)(x+3)=0
x=1/2或x=-3

4. X^2-3X-10=0
(x-5)(x+2)=0
x=5或x=-2

5.(X-3)(X+7)= -9
x^2+4x-12=0
(x+6)(x-2)=0
x=-6或x=2

6. (3Y-2)^2=(2Y-3)^2
(3y-2+2y-3)(3y-2-2y+3)=0
5(y-1)(y+1)=0
y=1或y=-1

7.(2Y+1)^2-8(2Y+1)+15=0
(2y+1-3)(2y+1-5)=0
4(y-1)(y-2)=0
y=1或y=2

8. (X-1)^2=2X(1-X)
(x-1)(x-1+2x)=0
(x-1)(3x-1)=0
x=1或x=1/3

Answer 3

1. X（2X＋1）＝3（2X+1)
（2X＋1）(X-3)=0
x1=-1/2 x2=3
2. (X-2)^2=2-X
(X-2)(x-2+1)=0
x1=2 x2=1
3. X(2X-1)=3(1-2X)
（2X-1）(X+3)=0
x1=1/2 x2=-3
4. X^2-3X-10=0
(x-5)(x+2)=0
x1=5 x2=-2
5.(X-3)(X+7)= -9
x^2+4x-21+9=0
x^2+4x-12=0
(x+6)(x-2)=0
x1=-6 x2=2
6. (3Y-2)^2=(2Y-3)^2
(3Y-2)^2-(2Y-3)^2=0
(3y-2+2y-3)(3y-2-2y+3)=0
5(y-1)(y+1)=0
y1=1 y2=-1
7.(2Y+1)^2-8(2Y+1)+15=0
(2Y+1-3)(2Y+1-5)=0
2(y-1)*2(y-2)=0
y1=1 y2=2
8. (X-1)^2=2X(1-X)
(X-1)(x-1+2x)=0
(x-1)(3x-1)=0
x1=1, x2=1/3

Answer 4

1. x(2x+1)-3(2x+1)=0
(x-3)(2x+1)=0
x=3 or x=-0.5

2. (x-2)^2-(2-x)=(x-2)^2+(x-2)=0
(x-2)(x-2+1)=0 (x-2)(x-1)=0
x=2 or x=1

3. x(2x-1)-3(1-2x)= x(2x-1)+3(2x-1)=0
(x+3)(2x-1)=0
x=-3 or x=0.5

4. (x-5)(x+2)=0
x=5 or x=-2

5. x^2+4x-21=-9 x^2+4x-12=0
(x-2)(x+6)=0
x=2 or x=-6

6. (3y-2)^2-(2y-3)^2=0
(3y-2+2y-3)(3y-2-2y+3)=0
(5y-5)(y+1)=0
y=1 or y=-1

7. 把2y+1看过一项， (2y+1-3)(2y+1-5)=0
y=1 or y=2

8. (x-1)^2-2x(1-x)= (x-1)^2+2x(x-1)= 0
(x-1)(x-1+2x)=0
x=1 or x=1/3