Question

若x²=3y+8,y²=-3x+8，且x+y≠0，则x³-y³值为

Answer 1

x^2=3y+8 (1)
y^2=-3x+8 (2)

(1)-(2)
(x+y)(x-y) = 3(x+y)
(x+y)(x-y+3)=0
x-y = 3

(1)+(2)
x^2+y^2 = -3(x-y)+16
= -9+16
=7

(x-y)=3
(x-y)^2 =9
x^2-2xy +y^2 =9
7-2xy =9
xy = -1

x^3-y^3
=(x-y)(x^2+xy+y^2)
=3(x^2+xy+y^2)
=3( 7 -1)
=18

Answer 2

若单项式3x³y^5次方与﹣4分之1a²b^n-3的次数相同
则3+5=2+n-3,
∴n=9,
-3n-6=-3*9-6=-33
2、若x²y²+x³-3xy³-mx³y³+8没有六次项,
则mx³y³的系数为0,即m=0