(1)设x属于R,试比较x^6与x^5-1的大小

问题描述:

(1)设x属于R,试比较x^6与x^5-1的大小
(2)在等比数列an和等差数列bn中,a1=b1>0.a3=b3>0,a1≠a3,试比较a5与b5的大小

设公比为q,公差为d,则2d=(b3-b1)=(a3-a1)/2,q^2=a3/a1
a5=a1q^4=a1(a3/a1)^2=[(a3)^2]/a1
b5=b1+4d=a1+2(a3-a1)=2a3-a1
a5-b5=[(a3)^2]/a1-(2a3-a1)=[(a3)^2-2a1a3+(a1)^2]/a1=(a3-a1)^2/a1
(a3-a1)^2>0,a1>0,所以a5-b5>0即a5>b5