Question

已知:a1/2+a-1/2=3 求解:(a3/2-a-3/2)/( a1/2-a-1/2)

Answer 1

a1/2+a-1/2=3
平方
a+2+a-1=9
a+a-1=7

原式分母是立方差
=( a1/2-a-1/2)(a+1+a-1)/( a1/2-a-1/2)
=a+1+a-1
=7+1
=8

Answer 2

a(n+1)-1/3=4an-1-1*3=4an-4/3
a(n+1)-1/3=4(an-1/3)
[a(n+1)-1/3]/(an-1/3)=4
所以an-1/3是等比数列

[a(n+1)-1/3]/(an-1/3)=4
所以q=4
a1-1/3=5/3
所以an=(5/3)*4^(n-1)