Question

初一的有理数四则混合运算，化简求值，一元一次方程

Answer 1

一元一次方程：
1.2(x-2)-3(4x-1)=9(1-x)
4x-4-12x+3=9-9x
-8x+9x=9-3+4
x=10
2.11x+64-2x=100-9x
11x-2x+9x=100-64
18x=36
x=2
3.15-(8-5x)=7x+(4-3x)
15-8+5x=7x+4-3x
5x-7x+3x=4-15+8
x=-3
4.3(x-7)-2[9-4(2-x)]=22
3x-21-2(9-8+4x)=22
3x-21-18+16-8x=22
-5x=22+23
-5x=45
x=-9
6.2(x-2)+2=x+1
2x-4+2=x+1
2x-x=1+4-2
x=3
7.0.4(x-0.2)+1.5=0.7x-0.38
0.4x-0.08+1.5=0.7x-0.38
-0.3x=0.08-0.38-1.5
-0.3x=-1.8
x=6
8.30x-10(10-x)=100
30x-100+10x=100
40x=200
x=5
9.4(x+2)=5(x-2)
4x+8=5x-10
x=18
10.120-4(x+5)=25
120-4x-20=25
4x=120-20-25
4x=75
x=18.75
11.15x+863-65x=54
-50x=-863-54
-50x=-917
x=58.64
12.12.3(x-2)+1=x-(2x-1)
12.3x-24.6+1=-x+1
4x=24.6
x=6.15
13.11x+64-2x=100-9x
9x+9x=100-64
18x=36
x=2
14.14.59+x-25.31=0
x-10.72=0
x=10.72
15.x-48.32+78.51=80
x+30.19=80
x=49.81
1.（3X+2Y)+(4X+3Y)其中X=5,Y+3
原式=3X+2Y+4X+3Y=7X+5Y
当X=5,Y=3时
原式=5*7+（-3）*5+20
2.(5a^2-3b^2)+(a^2+b^2)-(5a^2+3b^2),其中a=-1,b=1
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(-1)^2-5*1^2
=1-5
=-4
3.2(a^2b+ab^2)-2(a^2 b-1)-2ab^2 -2其中a=-2,b=2
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
化简求值附整体答案：
1、已知A,B是方程x^2+2x-5=0的两个实数根,
求(A^2+2AB+2A)(B^2+2AB+2B)的值.
由A,B是方程x^2+2x-5=0的两个实数根得：
AB=-5,A+B=-2
A^2+2AB+2A)(B^2+2AB+2B)
=AB（A+2B+2）（B+2A+2）
=-5（-2+B+2）（-2+A+2）
=-5AB
=25
2、1/2(x+y+z)方+1/2(x-y-z)(x-y+z)-z(x+y),其中x-y=6,xy=21.要详细步骤
化简得：
1/2(x+y+z)方+1/2(x-y-z)(x-y+z)-z(x+y)=
1/2[(x+y)方+2z(x+y)+z方]+1/2[(x-y)方-z方]-z(x+y)=
1/2(x+y)方+1/2(x-y)方=x方＋y方
由x-y=6,xy=21得,x方＋y方＝（x-y）方＋2xy＝78
3、a^2-ab+2b^2=3 求2ab-2a^2-4b^2-7的值
2ab-2a^2-4b^2-7
=2(ab-a^2-2b^2)-7
=-2(a^2-ab+2b^2)-7
=(-2)*3-7
=-6-7=-13
4、若A=2x^2+3xy-2x-3,B=-x^2+xy+2,且3A+6B的值与x无关,求y的值
3A+6B=6x^2+9xy-6x-9-6x^2+6xy+12
=15xy-6x+3
=x(15y-6)+3
5、9x+6x^2 -3(x-2/3x^2).其中x=-2
9x+6x² -3(x-2/3x²)
=9x+6x²-3x+2x²
=8x²+6x
=8×(-2)²+6×(-2)
=32-12
=20
6、1/4(-4x^2+2x-8)-(1/2x-1),其中x=1/2
1/4(-4x²+2x-8)-(1/2x-1)
=-x²+1/2x-2-1/2x+1
=-x²-1
=-(1/2)²-1
=-1/4-1
=-5/4
7、3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz,其中x=-2,y=-3,z=1,
:3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz
=3x'y-2x'y+2xyz-x'z+4x'z-xyz
=x'y-xyz+3x'z
=4*(-3)-2*3*1+3*4*1
=-12-6+12
=-6
8、(5a^2-3b^2)+(a^2+b^2)-(5a^2+3b^2),其中a=-1,b=1
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(-1)^2-5*1^2
=1-5
=-4
9、2(a^2b+ab^2)-2(a^2 b-1)-2ab^2 -2其中a=-2,b=2
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
10、(X-2分之1Y-1)(X-2分之1Y+1)-(X-2分之1Y-1)的平方
其中X=1.7,Y=3.9(先化简再求值)
[(X-2分之1Y)-1][(X+2分之1Y)+1]-(X-2分之1Y-1)平方
=(X+2分之1Y)平方-1-(X-2分之1Y)平方+2(X-2分之1Y)-1
=(X+2分之1Y)平方-(X-2分之1Y)平方+2(X-2分之1Y)-2
=2XY+2X-Y-2
=3.9*2.4+1.4
=10.76
11.（3X+2Y)+(4X+3Y)其中X=5,Y+3
原式=3X+2Y+4X+3Y=7X+5Y
当X=5,Y=3时
原式=5*7+（-3）*5+20
12.(5a^2-3b^2)+(a^2+b^2)-(5a^2+3b^2),其中a=-1,b=1
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(-1)^2-5*1^2
=1-5
=-4
13.2(a^2b+ab^2)-2(a^2 b-1)-2ab^2 -2其中a=-2,b=2
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
14.2a-（3a-2b+2）+（3a-4b-1) =（ ）,a=b=1
=2a-3a+2b-2+3a-4b-1
=（2-3+3）a+（2-4）b+（-2-1）
=2a-2b-3=-3
15.5-(1-x)-1-(x-1）,x=11
=5-1+x-1-x+1
=4
③2x-(x+3y)-(-x-y)-(x-y)=（ ）
=2x-x+3y+x+y-x+y
=x+5y