Question

Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\). Cmr: \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)

Answer 1

\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)

\(=\frac{a}{d}=\frac{c}{b}=\frac{b}{c}\)

\(=\frac{a+c+b}{d+b+c}\)

\(\Rightarrow\frac{a}{d}=\frac{c}{b}=\frac{b}{c}=\left(\frac{a+b+c}{b+d+c}\right)^3\)

\(\Rightarrow\frac{a}{d}=\left(\frac{a+b+c}{b+c+d}\right)^3\left(đpcm\right)\)

Answer 2

Cho \(\frac{a}{2003}=\frac{a}{2004}=\frac{c}{2005}\)

Chứng minh rằng: 4(a - b)(b - c) = (c - a)\(^2\)