\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{d}{e}=k\\ \Rightarrow a=bk;b=ck;c=dk;d=ek\\ \Rightarrow\left(\dfrac{2019b+2020c-2021d}{2019c+2020d-2021e}\right)^3=\left(\dfrac{2019.c.k+2020.d.k-2021e.k}{2019c+2020d-2021e}\right)^3\\ \Rightarrow\left(\dfrac{k\left(2019c+2020d-2021e\right)}{2019c+2020d-2021e}\right)^3=k^3\)
\(=\left(\dfrac{a}{b}\right)^2.\)\(\dfrac{b}{c}=\dfrac{a^2}{b^2}.\)\(\dfrac{b}{c}=\dfrac{a^2}{bc}\)
\(\left(đpcm\right)\)
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