Question

设x=（3=根号5）/2，y=(3-根号5)/2,求x平方+y平方

设x＝2分之3－根号5 y＝2分之3－根号5 求x立方－y的立方
不要看错，设x＝2分之3加根号5 y＝2分之3－根号5是求x的立方加y的立方，，，，

Answer 1

解：x＝(3 -√5)/2，y=(3+√5)/2
∴xy=(3 -√5)/2 *(3+√5)/2=(9-5)/4=1
x+y=3

x的立方加y的立方
=x³+y³
=(x+y)(x²-xy+y²)
=(x+y)[(x+y)²-3xy]
=3*[9-3*1]
=3*6
=18

【俊狼猎英】团队为您解答

Answer 2

x³+y³
=(x+y)(x²-xy+y²)
=[(3+√5)/2+(3-√5)/2] { [(3+√5)/2]²-(3+√5)/2×(3-√5)/2+[(3-√5)/2]² }
=3×[(9+6√5+5)/4-(3²-√5²)/4+(9-6√5+5)/4]
=3×[(14+6√5)/4-1+(14-6√5)/4]
=3×(7-1)
=18