Question

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

chứng minh \(\left(\dfrac{a+b+c}{b+c+d}\right)_3=\dfrac{a}{d}\)

giúp mình với

Answer 1

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

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

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

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

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

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

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