Question

配方法解一元二次方程

⒈把一元二次方程3X的平方-2X-3=0化成3（X+M）的平方=N的形式是？若多项式X的平方-AX+2A-3是一个完全平方式。则A=？
⒉将方程2X的平方+4X+1=0配方后，得到的新方程为
⒊用配方法解方程：
4X的平方-7X+2=0
⒋已知4X的平方-AX+1可变为（2X-B）的平方的形式，则AB=？
⒌用配方法解3X的平方-8X=3的解为？
⒍已知X=二分之一（根号7+根号5），Y=二分之一（根号7-根号5），求X的平方-XY+Y的平方的值
⒎将2Y的平方-6Y+1配方

Answer 1

1.
3X^2-2X-3=0
3(X^2-2/3X-1)=0
3[(X^2-2/3X+1/9)-1/9-1]=0
3[(X-1/3)^2-10/9]=0
3(X-1/3)^2-10/3=0
所以3(X+M)^2=N的形式是3(X-1/3)^2=10/3

X^2-AX+2A-3
△=b^2-4ac
=(-A)^2-4*1*(2A-3)
=A^2-4(2A-3)
=A^2-8A+12
A^2-8A+12=(A-2)(A-6)
A1=2,A2=6
则A=2,6

2.
2X^2+4X+1=0
2(X^2+2X+1/2)=0
2[(X^2+2X+1)-1+1/2]=0
2[(X+1)^2-1/2]=0
2(X+1)^2-1=0

3.
4X^2-7X+2=0
(X^2-7/4X+1/2)=0
[(X^2-7/4X+49/64)-49/64+1/2]=0
(X-7/8)^2-17/64=0
(X-7/8)^2=17/64
X-7/8=正负根号17/8
X=7/8加减根号17/8
X1=(7+根号17)/8
X2=(7-根号17)/8

4.
4X^2-AX+1=(2X-1)^2
(2X-1)^2=4X^2-4X+1
则A=4

5.
3X^2-8X=3
3X^2-8X-3=0
X^2-8/3X-1=0
(X^2-8/3X+16/9)-16/9-1=0
(X-4/3)^2-25/9=0
(X-4/3)^2=25/9
X-4/3=正负5/3
X=4/3加减5/3
X1=(4+5)/3=3
X2=(4-5)/3=-1/3

6.
X+Y=根号7
XY=1

X^2-XY+Y^2
=X^2+Y^2-XY
=(X+Y)^2-2XY-XY
=(X+Y)^2-3XY
=(根号7)^2-3*1
=7-3
=4

7.
2Y^2-6Y+1
=2(Y^2-3Y+1/2)
=2[(Y^2-3Y+9/4)-9/4+1/2]
=2[(Y-3/2)^2-7/4]
=2(Y-3/2)^2-7/2

Answer 2

1.
3X^2-2X-3=0
3(X^2-2/3X-1)=0
3[(X^2-2/3X+1/9)-1/9-1]=0
3[(X-1/3)^2-10/9]=0
3(X-1/3)^2-10/3=0
所以3(X+M)^2=N的形式是3(X-1/3)^2=10/3

X^2-AX+2A-3
△=b^2-4ac
=(-A)^2-4*1*(2A-3)
=A^2-4(2A-3)
=A^2-8A+12
A^2-8A+12=(A-2)(A-6)
A1=2,A2=6
则A=2,6

2.
2X^2+4X+1=0
2(X^2+2X+1/2)=0
2[(X^2+2X+1)-1+1/2]=0
2[(X+1)^2-1/2]=0
2(X+1)^2-1=0

3.
4X^2-7X+2=0
(X^2-7/4X+1/2)=0
[(X^2-7/4X+49/64)-49/64+1/2]=0
(X-7/8)^2-17/64=0
(X-7/8)^2=17/64
X-7/8=正负根号17/8
X=7/8加减根号17/8
X1=(7+根号17)/8
X2=(7-根号17)/8

4.
4X^2-AX+1=(2X-1)^2
(2X-1)^2=4X^2-4X+1
则A=4

5.
3X^2-8X=3
3X^2-8X-3=0
X^2-8/3X-1=0
(X^2-8/3X+16/9)-16/9-1=0
(X-4/3)^2-25/9=0
(X-4/3)^2=25/9
X-4/3=正负5/3
X=4/3加减5/3
X1=(4+5)/3=3
X2=(4-5)/3=-1/3

6.
X+Y=根号7
XY=1

X^2-XY+Y^2
=X^2+Y^2-XY
=(X+Y)^2-2XY-XY
=(X+Y)^2-3XY
=(根号7)^2-3*1
=7-3
=4

7.
2Y^2-6Y+1
=2(Y^2-3Y+1/2)
=2[(Y^2-3Y+9/4)-9/4+1/2]
=2[(Y-3/2)^2-7/4]
=2(Y-3/2)^2-7/2

Answer 3

解：1. 3(x-0.75)^2=57/16
2或6
2. 2（x+1）^2-1=0
3. 2或-4
4. 4
5. 3或-1/3
6.11/2
7.2（y-1.5）^2-7/2

Answer 4

数学