已知A=根号3+根号5，B=根号3-根号5，求A的三次方+B的三次方的整数部分

A=√3+√5
B=√3-√5
A^3+B^3
=(A+B)(A^2-AB+B^2)
=(A+B)(A^2+2AB+B^2-3AB)
=(A+B)[(A+B)^2-3AB]
=(√3+√5+√3-√5)[(√3+√5+√3-√5)^2-3(√3+√5)(√3-√5)]
=2√3*[(2√3)^2-3*(3-5)]
=2√3*[12+6]
=36√3
1<√3<2
36<36√3<72
A^3+B^3的整数部分为：62

A=√(3+√5)
=√[2*(6+2√5)/4]
=√[2(√5+1)^2/4]
=(√5+1)/2*√2
=(√10+√2)/2
B=√3-√5
=√[2*(6-2√5)/4]
=√[2(√5-1)^2/4]
=(√5-1)/2*√2
=(√10-√2)/2

A^3+B^3
=(A+B)(A^2-AB+B^2)
=(A+B)(A^2+2AB+B^2-3AB)
=(A+B)[(A+B)^2-3AB]
=[(√10+√2)/2+(√10-√2)/2]{[(√10+√2)/2+(√10-√2)/2]^2-3*(√10+√2)/2*(√10-√2)/2}
=√10*{(√10)^2-6}
=4√10
3<√10<4
9<3√10<12
A^3+B^3的整数部分为：9

a^3+b^3=(a+b)(a^2+b^2-ab)
a+b=2根号3
ab=-2
(a+b)^2=a^2+b^2+2ab
12=a^2+b^2-4
a^2+b^2=16
a^3+b^3=(a+b)(a^2+b^2-ab)=36根号3

A+B=2√5 A-B=2√5 AB=-2
A³+B³
=(A+B)(A²-AB+B²)
=(A+B)[(A-B)²+AB]
=2√3×[(2√5)²-2]
=2√3×[20-2)
=2√3×18
=36√3
≈62.352