Question

设x=2+根号3/2-根号3，y=2-根号3/2+根号3，求x的3次方+y的3次方的值 要简便算法 不要死算

Answer 1

x=2+根号3/2-根号3=(2+√3)²/(2+√3)(2-√3)=7+4√3
y=……=7-4√3
x+y=14
xy=1
x³+y³=(x+y)(x²-xy+y²)=(x+y)[(x+y)²-3xy]
=14×(14²-3)
=2702

Answer 2

x+y=4
xy=4-(根号3/2-根号3)的平方=3√2-1/2
x的3次方+y的3次=(x+y)(x^-xy+y^)
=4[(x+y)^-3xy]
=4(16-9√2+3/2)
=70-36√2

Answer 3

x=(2+√3)/2-√3=(2-√3)/2
y=(2-√3)/2+√3=(2+√3)/2
x^3+y^3
=(x+y)(x^2-xy+y^2)
=2*[(2-√3)^2/4-(2-√3)(2+√3)/4+(2+√3)^2/4]
=(2/4)*[4+3-2√3-3+4+4+3+2√3]
=(1/2)*15
=15/2
有不懂欢迎追问