Question

Answer 1

-Đặt \(a=2000;b=22;c=2022\Rightarrow a+b=c\)

\(\dfrac{2022^3+22^3}{2022^3+2000^3}= \dfrac{c^3+b^3}{c^3+a^3}=\left(\dfrac{c+b}{c+a}\right)\left(\dfrac{c^2-cb+b^2}{c^2-ca+a^2}\right)=\left(\dfrac{c+b}{c+a}\right)\left(\dfrac{\left(a+b\right)^2-\left(a+b\right)b+b^2}{\left(a+b\right)^2-\left(a+b\right)a+a^2}\right)=\left(\dfrac{c+b}{c+a}\right)\left(\dfrac{a^2+2ab+b^2-ab-b^2+b^2}{a^2+2ab+b^2-a^2-ab+a^2}\right)=\left(\dfrac{c+b}{c+a}\right)\left(\dfrac{a^2+ab+b^2}{a^2+ab+b^2}\right)=\dfrac{c+b}{c+a}=\dfrac{2022+22}{2022+2000}\left(đpcm\right)\)