Đặt \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{e}=k\)
=>\(\begin{cases}d=ek\\ c=d\cdot k=ek\cdot k=ek^2\\ b=ck=ek^2\cdot k=ek^3\\ a=bk=ek^3\cdot k=ek^4\end{cases}\)
\(\left(\frac{2019b+2020c-2021d}{2019c+2020d-2021e}\right)^3\)
\(=\left(\frac{2019\cdot ek^3+2020\cdot ek^2-2021\cdot ek}{2019\cdot ek^2+2020\cdot ek-2021\cdot e}\right)^3\)
\(=\left\lbrack ek\cdot\frac{\left(2019k^2+2020k-2021\right)}{e\left(2019k^2+2020k-2021\right)}\right\rbrack^3=k^3\)
\(\frac{a^2}{bc}=\frac{a}{b}\cdot\frac{a}{c}=\frac{ek^4}{ek^3}\cdot\frac{ek^4}{ek^2}=k\cdot k^2=k^3\)
Do đó: \(\left(\frac{2019b+2020c-2021d}{2019c+2020d-2021e}\right)^3=\frac{a^2}{bc}\)
