（m+n)x^2+2xy(n-2m)+(4m+n)y^2

解
z²-x²+2xy-y²
=z²-(x²-2xy+y²)
=z²-(x-y)²
=(z+x-y)(z-x+y)

x1=dsolve('(x^2+2*x*y-y^2)+(y^2+2*x*y-x^2)*Dy=0','y(1)=1','x')
x1 =
1/2+1/2*(1+4*x-4*x^2)^(1/2)
x2=dsolve('D2x+2*n*Dx+a^2*x=0','x(0)=x0,Dx(0)=V0','t')
x2 =
1/2*(n*x0+(n^2-a^2)^(1/2)*x0+V0)/(n^2-a^2)^(1/2)*exp((-n+(n^2-a^2)^(1/2))*t)-1/2*(n*x0-(n^2-a^2)^(1/2)*x0+V0)/(n^2-a^2)^(1/2)*exp((-n-(n^2-a^2)^(1/2))*t)

x-y-x^2+2xy-y^2+2=0
(x-y)-(x-y)^2+2=0
(x-y)^2-(x-y)-2=0
(x-y-2)(x-y+1)=0
x=2+y
x=y-1
2x+2y=20
4+2y+2y=20
y=4
x=6
面积s=24
2y-2+2y=20
y=5.5（舍去）

gradf=(2x+2y,2x)
gradp=(4,2)
l方向的单位向量为l0=(1/√2,1/√2)
所以gradl=gradp*l0=4x(1/√2)+2x(1/√2)=3√2

x/y=2
x=2y
原式=(x+3y)(x-3y)/(x+3y)(x-y)
=(x-3y)/(x-y)
=(2y-3y)/(2y-y)
=-y/y
=-1

1.原式=x^n（x^2-x-1）
2.x y 常数
1 4 -3
1 -2 2
∴原式=（x+4y-3）（x-2y+2）
3.这道题是让我解方程吗?
n^2+n^2（n+1）^2+(n+1)^2=n^4+(n+1)^2+2n^2(n+1)
n^2+n^4+2n^3+n^2=n^4+2n^3+2n^2
0=0
∴x为任意实数
4.原式=1+2+2*3^1+2*3^2+.+2*3^2010
=1+2*(1+3^1+3^2+.+3^2010)
=1+2*(3^2011-1)/2
=3^2011
5.正确的是（1）（4）
（1）2=1×2
∴F(2)=1/2正确
（2）24=1×24=2×12=3×8=4×6
∴F(24)=4/6=2/3错误
（3）27=1×27=3×9
∴F(27)=3/9=1/3错误
（4）∵n为完全平方数
∴n=√n×√n（n为正整数）
∴F(n)=√n/√n=1正确

1.y^2+2xy+x^2=(x+y)^2
2.ab
3.4x+2（根号x） 怕你看不懂
4.186
5.m^2+n^2+2mn-6m-6n+9

x^2+2xy-ax+y^2-ay+25
=(x^2+2xy-y^2)-a(x+y)+25
=(x+y)^2-a(x+y)+25
=(x+y)^2-a(x+y)+a^2/4-a^2/4+25
=(x+y-a/2)^2-a^2/4+25
因为是完全平方
则
-a^2/4+25=0
a^2=100
a=±10

2(A+X^2-XY-Y^2)=X^2+2XY-3Y^2
2A=4XY-X^2-Y^2
A=2XY-二分之一X^2-二分之一Y^2

即-(x-y)²+(x-y)+2=0
(x-y)-(x-y)-2=0
(x-y-2)(x-y+1)=0
x-y>0
所以x-y=2
周长2(x+y)=16
x+y=8
所以x=5,y=3
所以面积=xy=15平方厘米

根据周长(X + Y )*2 = 16
得
X + Y = 8
X = 8 - Y 代入后式整理得：
4Y^2 -30Y + 54 = 0
即（Y - 3）（4Y - 18） = 0
解得
Y = 3 或4.5（舍弃）
因此X = 8- 3 = 5
面积 = 5*3 = 15 平方厘米

x^2+2xy-3y^2=0
x^2+2xy+y^2-4y^2=0
(x+y)^2=4y^2
x+y=2y或x+y=-2y
x=y或x=-3y
因为两个正实数
所以x=y
x^2+xy+y^2/x^2-xy+y^2
=（x^2+x^2+x^2)/(x^2-x^2+x^2)
=3x^2/(x^2)
=3

(X^2-2XY+Y^2+3)(-X^2+2XY-Y^2+3)
提一个负号出来：
=-(X^2-2XY+Y^2+3)(X^2-2XY+Y^2-3)
=-[（x-y)^2+3][(x-y)^2-3]
设(x-y)^2=A
那么,原式=-（A+3）（A-3）=(3+A)(3-A).
因此,A=(x-y)^2.

[x(x+y)/2(x+2y)]X[3(x-y)/x(x+2y)]X[(x+2y)(x+2y)/3(x+y)(x-y)]=1/2

x-y-x^2+2xy-y^2+6
=x-y-(x^2-2xy+y^2)+6
=x-y-(x-y)^2+6
=-[-(x-y)+(x-y)^2-6]
=[(x-y)^2-(x-y)-6]
=-[(x-y-3)(x-y+2)]
=-(x-y-3)(x-y+2)
所以X-Y=3或 X-Y=-2
长方形的周长为20cm
所以X+Y=10
当X-Y=3 时 X=6.5 Y=3.5 由于x,y都是整数 所以舍去
当X-Y=-2是 X=4 Y=6 所以面积是4*6＝24

1.x^2+2xy-x-y+y^2-2
=x^2-1+y^2-1+xy-x+xy-y
=(x+1)(x-1)+(y+1)(y-1)+x(y-1)+y(x-1)
=(x+y+1)(x-1)+(x+y+1)(y-1)=(x+y+1)(x+y-2)
2.x^2-2xy+3x-3y+y^2+2
=x^2-1+y^2-1+x-xy-y-xy+2x+2-2y+2
=(x+1)(x-1)+(y+1)(y-1)-x(y-1)-y(x+1)+2(x+1)-2(y-1)
=(x+1)(x-y+1)+(y-x-1)(y-1)=(x-y+1)(x-y+2)

1
y'+y/x=x^2y^6
xdy+ydx=y^6x^3dx
dxy=y^6x^3dx
xy=u
du=u^6dx/x^3
du/u^6=dx/x^3
-(1/5) *(1/u^5)=(-1/2)*(1/x^2)+C
1/u^5=(5/2)(1/x^2)+C1 c1=-5c
通解1/y^5=(5/2)x^3+C1x^3
2
(x^2+2xy-y^2)dx+(y^2+2xy-x^2)dy=0
(x^2/y^2+2x/y--1)dx+(1+2x/y-x^2/y^2)dy=0
x=yu dx=ydu+udy
(u^2+2u-1)(ydu+udy)+(1+2u-u^2)dy=0
(u^2+2u-1)ydu+(u^3+2u^2-u+1+2u-u^2)dy=0
(u^2+2u-1)ydu+(u^3+u^2+u+1)dy=0
(u^2+2u-1)du/(u^3+u^2+u+1)=-dy/y
(u^2+u-1)du/(u+1)(u^2+1)=-dy/y
(u^2+u-1)/[(u+1)(u^2+1)]= A/(u+1)+(Bu+C)/(u^2+1)
A(u^2+1)+Bu^2+Cu=u^2+u-1
A=-1 B=2,C=1
∫(u^2+u-1)du/(u+1)(u^2+1)=∫-du/(u+1)+∫(2u+1)du/(u^2+1)
=-ln|u+1|+ln|u^2+1|+arctanu
-ln|u+1|+ln|u^2+1|+arctanu=-lny+C
通解 -ln|x/y +1|+ln|x^2/y^2 +1| +arctan(x/y)=-lny+C

因为多项式(m-2)x^2+2xy-y^2+3x^2-x+1=(m+1)x^2+2xy-y^2-x+1中不含x^2项
所以(m+1)=0
所以m=-1
所以3m^3-m^2004+1=-3-(-1)^2004+1=-3-1+1=-3.
所以3m^3-m^2004+1的值为3.

由x-y-x^2+2xy-y^2+2=0整理得(x-y+1)(x-y-2)=0
∴x-y=-1或x-y=2
∵长方形周长为16cm,它的长为x 宽为y
∴2(x+y)=16
解方程组得x=3.5,y=4.5或x=5,y=3
∵长方形的长为x 宽为y 都是整数
∴x=5,y=3
∴长方形的面积=长*宽=xy=15

12/7
先移项,变成x＝3y
再带入就可以算出来了

x-y-x²+2xy-y²+2=0
x=y-1 或者 x=y+2
x=5,y=3 面积为xy=15平方厘米
或x=3.5 ,y=4.5 积为15.75平方厘米

（x^2+2xy-3y^2)/(x-y）
=(x+3y)(x-y)/(x-y)
=x+3y
=12.5

左边的式子分别对X、y求导,求导X时y当成已知量,同理对Y求导