Question

Cho a/b = b/c = c/d Chứng minh (a+b+c/b+c+d)^3 = a/d

Answer 1

Ta có :

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

Áp dụng t/c dãy tỉ số bawg nhau ta có :

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

\(\Leftrightarrow\left(\dfrac{a}{b}\right)^3=\left(\dfrac{b}{c}\right)^3=\left(\dfrac{c}{d}\right)^3=\left(\dfrac{a+b+c}{b+c+d}\right)^3=\dfrac{a}{b}.\dfrac{a}{b}.\dfrac{a}{b}=\dfrac{b}{c}.\dfrac{b}{c}.\dfrac{b}{c}=\dfrac{c}{d}.\dfrac{c}{d}.\dfrac{c}{d}=\dfrac{a}{d}\)

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