Question

[Vu Hai Anh]

\(Cho:\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{a}\) biết \(a=b=c=d\). Tính tổng \(M=\frac{2a-b}{c+d}+\frac{2b-c}{a+d}+\frac{2c-d}{a+d}+\frac{2d-a}{b+c}\)

Answer 1

[Nguyễn Linh Chi]

Biết a=b=c=d 

Thay vào M

Ta có: 

\(M=\frac{2a-a}{a+a}+\frac{2a-a}{a+a}+\frac{2a-a}{a+a}+\frac{2a-a}{a+a}\)

\(=4.\frac{2a-a}{a+a}=4.\frac{a}{2a}=4.\frac{1}{2}=2\)