Question

Cho a/b = b/c = c/d . Cmr : ( a+b+c / b+c+d )^3 = a/d .

Answer 1

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

=>\(\left\{{}\begin{matrix}c=dk\\b=ck\\a=bk\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}c=dk\\b=dk\cdot k=dk^2\\a=dk^2\cdot k=dk^3\end{matrix}\right.\)

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

\(=\left(\dfrac{dk\left(k^2+k+1\right)}{d\left(k^2+k+1\right)}\right)^3=k^3\)

\(=\dfrac{dk^3}{d}=\dfrac{a}{d}\)