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Question Number 163143 by amin96 last updated on 04/Jan/22

Commented by HongKing last updated on 04/Jan/22

r^2  = r + 2021 + 2021^2   r^2  - r - 2021^2  - 2021 = 0  r = - 2021 ; 2022 ⇒ r = 2022 ✓

$$\mathrm{r}^{\mathrm{2}} \:=\:\mathrm{r}\:+\:\mathrm{2021}\:+\:\mathrm{2021}^{\mathrm{2}} \\ $$$$\mathrm{r}^{\mathrm{2}} \:-\:\mathrm{r}\:-\:\mathrm{2021}^{\mathrm{2}} \:-\:\mathrm{2021}\:=\:\mathrm{0} \\ $$$$\mathrm{r}\:=\:-\:\mathrm{2021}\:;\:\mathrm{2022}\:\Rightarrow\:\mathrm{r}\:=\:\mathrm{2022}\:\checkmark \\ $$

Commented by mr W last updated on 04/Jan/22

r_(n+1) =r_n +1  see Q64112

$${r}_{{n}+\mathrm{1}} ={r}_{{n}} +\mathrm{1} \\ $$$${see}\:{Q}\mathrm{64112} \\ $$

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