Question

初二数学问题，急

已知，a+b=1,ab=-1,设s1=a+b,s2=a^2+b^2,s3=a^3+b^3…Sn=a^n+b^n
计算s1= s2= s3= s4=
(2)试写出Sn-2,Sn-1,S三者之间的关系式

Answer 1

s1= 1 s2=3 s3= 4 s4=7
(2)试写出Sn-2,Sn-1,S三者之间的关系式
(sn-2)+(sn-1)=s n

Answer 2

1.S1=a+b=1
S2=a^2+b^2=(a+b)^2-2ab=3
S3=a^3+b^3=(a+b)^3-3ab(a+b)=4
S4=a^4+b^4=(a^2+b^2)^2-2(ab)^2=7

2. Sn-2+Sn-1=Sn