只要你上过初中就会做的II①：已知a+b=1 ab= —1 设S1=a+b ；S2=a2+b2；S3=a3+b3,……Sn=a的n次方+b的n次方（1）计算S1=；S2=;S3=;S4=（2）试写出Sn-2、Sn-1、Sn.三者之间的关系（3）根据以上结论,计算 a的七次方+b的七次方另有一作图题,+扣扣1679130480=
2019-05-27
只要你上过初中就会做的II
①：已知a+b=1 ab= —1 设S1=a+b ；S2=a2+b2；S3=a3+b3,……Sn=a的n次方+b的n次方
（1）计算S1=________；S2=_______;S3=_________;S4=_______
（2）试写出Sn-2、Sn-1、Sn.三者之间的关系_________________________
（3）根据以上结论,计算 a的七次方+b的七次方
另有一作图题,+扣扣
1679130480
=
优质解答
(1)
S1 = a+b = 1
S2 = a^2+b^2 = (a+b)^2 -2ab = 1 +2 = 3
S3 = a^3+b^3 = (a+b)(a^2-ab+b^2) =1*(S2 -ab) = 3+1 = 4
S4 = a^4+b^4 = (a^2+b^2)^2 -2a^2b^2 = (S2)^2 -2(ab)^2 =9 -2 =7
(2) Sn = Sn-2 + Sn-1
(3) 根据（1）和（2）的结果,
S5 = S4+S3 = 7+4 = 11
S6 = S5+S4 = 11+7 =18
S7 = S6+S5 = 18+11=29
即 a^7 + b^7 =29
(1)
S1 = a+b = 1
S2 = a^2+b^2 = (a+b)^2 -2ab = 1 +2 = 3
S3 = a^3+b^3 = (a+b)(a^2-ab+b^2) =1*(S2 -ab) = 3+1 = 4
S4 = a^4+b^4 = (a^2+b^2)^2 -2a^2b^2 = (S2)^2 -2(ab)^2 =9 -2 =7
(2) Sn = Sn-2 + Sn-1
(3) 根据（1）和（2）的结果,
S5 = S4+S3 = 7+4 = 11
S6 = S5+S4 = 11+7 =18
S7 = S6+S5 = 18+11=29
即 a^7 + b^7 =29