{1/xn}是调和数列,
1/(1/x(n+1)) -1/(1/xn)=d
x(n+1)-xn=d,为定值,即数列{xn}为等差数列,设公差为d
x1+x2+...+x9=9x1+36d=9(x1+4d)=9a5=90
a5=10
x3x7=(a5-2d)(a5+2d)=(10-2d)(10+2d)=100-4d²
平方项恒非负,d²≥0 4d²≥0
100-4d²≤100
x3x7的最大值是100,此时d=0