Bài 4: Cho các số thực a; b; c; d; e khác 0 thỏa mãn: $\frac{a}{b}$ =$\frac{b}{c}$ =$\frac{c}{d}$ =$\frac{d}{e}$  Chứng minh $\frac{2a^4+3b^4+2021.e^4+2022.d^4}{2b^4+3c^4+2021.d^4+2022.e^4}$ = $\frac{a}{e}$ 

Giải thích các bước giải:

Ta có:

$\dfrac{a}b=\dfrac{b}c=\dfrac{c}d=\dfrac{d}e$

$\to \dfrac{a^4}{b^4}=\dfrac{b^4}{c^4}=\dfrac{c^4}{d^4}=\dfrac{d^4}{e^4}=\dfrac ab\cdot\dfrac bc\cdot\dfrac cd\cdot\dfrac de=\dfrac ae$

$\to \dfrac ae= \dfrac{a^4}{b^4}=\dfrac{b^4}{c^4}=\dfrac{c^4}{d^4}=\dfrac{d^4}{e^4}$

$\to \dfrac ae= \dfrac{2a^4}{2b^4}=\dfrac{3b^4}{3c^4}=\dfrac{2021c^4}{2021d^4}=\dfrac{2022d^4}{2022e^4}=\dfrac{2a^4+3b^4+2021c^4+2022d^4}{2b^4+3c^4+2021d^4+2022e^4}$