Question

已知x=2+根号3，y=2-根号3，试求x*y与x²+y²的值。

根号2x+2=x+2根号2

Answer 1

xy=(2+根号下3)×(2-根号下3)
=4-(根号下3)²
=4-3
=1
x²+y²=(x+y)²-2xy
=(2+根号下3+2-根号下3)²-2
=16-2
=14
2x+2=x+2根号下2
x=2根号下2-2

追问

解方程：根号2x+2=x+2根号2

追答

根号下2x+2=x+2根号下2
x(根号下2-1)=2(根号下2-1)
x=2

Answer 2

xy=(2+√3)(2-√3)
=4-3
=1
x²+y²
=(x+y)²-2xy
=4²-2
=14

Answer 3

xy=(2+根号下3)×(2-根号下3)
=4-(根号下3)²
=4-3
=1 (抄一楼的)
x²+y²=(x+y)^2-2xy=4^2-2=14

Answer 4

x*y=1
x²+y²=14