Question

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

Answer 1

a/b=b/c=c/d=a+b+c/b+c+d=a mu 3+bmu 3+c mu 3/b mu 3+c mu 3+d mu 3=a/d

Answer 2

Ta có : \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

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

=> \(\left(\dfrac{a}{b}\right)^3\)=\(\left(\dfrac{a+b+c}{b+c+d}\right)^3\)(1)

mà \(\left(\dfrac{a}{b}\right)^3\)= \(\dfrac{a}{b}.\dfrac{a}{b}.\dfrac{a}{b}\)=\(\dfrac{a}{b}.\dfrac{b}{c}.\dfrac{c}{d}\)=\(\dfrac{a}{d}\)(2)

Từ (1);(2)=> \(\left(\dfrac{a+b+c}{b+c+d}\right)^3\)=\(\dfrac{a}{d}\)