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

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

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{b}=\dfrac{a+b+c}{b+c+d}\\\dfrac{b}{c}=\dfrac{a+b+c}{b+c+d}\\\dfrac{c}{d}=\dfrac{a+b+c}{b+c+d}\end{matrix}\right.\)

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

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

Answer 2

bn cũng có thể tham khảo

https://hoc24.vn/hoi-dap/question/466226.html