1;若X+Y=1,X^2=Y^2=3.求X^3+Y^32;若2X^2+3XY-2Y^2-X+8Y-6可以写成(X+2Y+M)(2X-Y+N)的形式,求(M^3+1)/(N^2-1)3;方程X^2-Y^2=1991,共有几组4;设A+B+2C=1,A^2+B^2-8C^2+6C=5,求AB-BC-CA

Question

1;若X+Y=1,X^2=Y^2=3.求X^3+Y^3
2;若2X^2+3XY-2Y^2-X+8Y-6可以写成(X+2Y+M)(2X-Y+N)的形式,求(M^3+1)/(N^2-1)
3;方程X^2-Y^2=1991,共有几组
4;设A+B+2C=1,A^2+B^2-8C^2+6C=5 ,求AB-BC-CA

Answer 1

(x+y)^2=(x^2+2xy+y^2)=1
xy=-5/2
x^3+y^3=(x+y)(x^2-xy+y^2)=17/2
2.
(X+2Y+M)(2X-Y+N)=2x^2+3xy+(N+2M)x-2y^2+(2N-M)y+MN
所以 N+2M=-1 2N-M=8
N=3 M=-2
(M^3+1)/(N^2-1) =-7/3
3.(x+y)(x-y)=1991
1991/11=181
x+y=11
x-y=181
得x=96 y=-85
或者
x+y=181
x-y=11
x=74 y=85
4.不知道