Question

[Đình Nguyên :v]

Cho dãy tỉ số bằng nhau \(\dfrac{a}{2019}\) = \(\dfrac{b}{2021}\) =  \(\dfrac{c}{2023}\). Chứng minh rằng \(\dfrac{\left(a-c\right)^2}{4}\) = (a - b)(b - c)

Answer 1

[Nguyễn Lê Phước Thịnh]

Đặt a/2019=b/2021=c/2023=k

=>a=2019k; b=2021k; c=2023k

(a-c)^2/4=(2023k-2019k)^2/4=(4k)^2/4=4k^2

(a-b)(b-c)=(2019k-2021k)(2021k-2023k)=4k^2

=>(a-c)^2/4=(a-b)(b-c)