Question

cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\) chứng minh \(\left(\dfrac{a+b+c}{b+c+d}\right)^3=\dfrac{a}{d}\)

Answer 1

Lời giải:

Áp dụng tính chất dãy tỉ số bằng nhau:

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

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

Lại có: \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\Rightarrow \left(\frac{a}{b}\right)^3=\frac{a}{b}.\frac{b}{c}.\frac{c}{d}\)

\(\Leftrightarrow \left(\frac{a}{b}\right)^3=\frac{a}{d}(**)\)

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