已知x+y=1,x^3+3x²+3x+3y-3y²+y^3=37,则（x+1）^4+(y-1)^4=?已知x+y=1,x的³+3x²+3x+3y-3y²+y的³=37,则（x+1）^4+(y-1)^4=?A.337 B.17 C.97 D.1

已知x+y=1,x^3+3x²+3x+3y-3y²+y^3=37,则（x+1）^4+(y-1)^4=?已知x+y=1,x的³+3x²+3x+3y-3y²+y的³=37,则（x+1）^4+(y-1)^4=?A.337 B.17 C.97 D.1
已知x+y=1,x^3+3x²+3x+3y-3y²+y^3=37,则（x+1）^4+(y-1)^4=?
已知x+y=1,x的³+3x²+3x+3y-3y²+y的³=37,则（x+1）^4+(y-1)^4=?
A.337 B.17 C.97 D.1

已知x+y=1,x^3+3x²+3x+3y-3y²+y^3=37,则（x+1）^4+(y-1)^4=?已知x+y=1,x的³+3x²+3x+3y-3y²+y的³=37,则（x+1）^4+(y-1)^4=?A.337 B.17 C.97 D.1
d 我没有啥好方法 把x=1-y带入 解下来 两组解下来 x=-4 y=5 或x=3 y=-2 正好 算下来一样

x^3+3x^2+3x+3y-3y^2+y^3=37 (1)
(x+y)^3=x^3+3x^2y+3xy^2+y^3=1 (2)
(1)-(2)
3x^2-3x^2y-3y^2-3xy^2+3(x+y)=36
3(x+y)(x-y)-3xy(x+y)+3(x+y)=36 x+y=1
x-y-xy+1=12
x(1-y)+(1-y)=12

全部展开

x^3+3x^2+3x+3y-3y^2+y^3=37 (1)
(x+y)^3=x^3+3x^2y+3xy^2+y^3=1 (2)
(1)-(2)
3x^2-3x^2y-3y^2-3xy^2+3(x+y)=36
3(x+y)(x-y)-3xy(x+y)+3(x+y)=36 x+y=1
x-y-xy+1=12
x(1-y)+(1-y)=12
(x+1)(1-y)=12 1-y=x
x^2+x-12=0
(x+4)(x-3)=0
x=-4 或3 x+1=-3或4 y-1=4或-3
(x+1)^4+(y-1)^4=3^4+4^4=337
选 A

收起