Question

数学代数题

已知x+y=1 求x三次方+y三次方+3xy的值

我要的是过程

Answer 1

x+y=1得出
(x+y)³=1
分解之后为 x³+3x²y+3xy²+y³=1
x³+y³+3xy(x+y)=1
因为x+y=1，所以x³+y³+3xy(x+y)=1即为x³+y³+3xy=1

Answer 2

边化简边代入
x^3+y^3+3xy
=(x+y)(x^2-xy+y^2)+3xy
=(x+y){(x+y)^2-3xy}+3xy
=1-3xy+3xy
=1

Answer 3

已知x+y=1所以(X+Y)3=1 得X3+3x2y+3xy2+Y3=1 得x3+y3+3XY(X+Y)=1 得x3+y3+3xy=1

Answer 4

（X+Y)^3=X^2+Y^3+3X^2Y+3XY^2
=X^3+Y^3+3XY(X+Y)
(X+Y0^3=X^3+Y^3+3XY(X+Y)
当X+Y=1时，（X+Y）^3=X^3+y^3+3XY*1
所以X^3+Y^3+3XY=1

Answer 5

x³+y³+3xy=(x+y)³-3xy(x+y-1)=1