在等差数列{an}中a1大于0,a2a4+2a3a5+a4a6=25求a3+a5的值
问题描述:
在等差数列{an}中a1大于0,a2a4+2a3a5+a4a6=25求a3+a5的值
答
a2a4+2a3a5+a4a6=(a3-d)(a3+d)+2a3a5+(a5-d)(a5+d)=(a3)^2-d^2+2a3a5+(a5)^2-d^2=(a3)^2+2a3a5+(a5)^2-2d^2=(a3+a5)^2-2d^2=25 因an>0,a1>0,d>0(a3+a5)^2-2d^2=25 a3+a5=√(25+2d^2)