Question

156009是四个连续奇数的积,求他们的和

Answer 1

(2x-3) (2x-1) (2x+1) (2x+3)=156009

(4x^2-1)(4x^2-9)=156009

令x^2=t得

(4t-1)(4t-9)=156009

16t^2-40t+9=156009

16t^2-40t=156000

4t^2-10t=39000

(2t-2.5)^2=39006.25

t=100

x=10

所以这4个连续奇数的和为80