Question Number 200357 by ajfour last updated on 17/Nov/23
Commented by ajfour last updated on 17/Nov/23
$$\:\:\:\:\:\:{Find}\:{r},\:{if}\:{square}\:{side}\:{is}\:{unity}. \\ $$
Commented by Frix last updated on 17/Nov/23
$$\mathrm{I}\:\mathrm{get}\:\mathrm{2}\:\mathrm{solutions}\:\left(\mathrm{did}\:\mathrm{not}\:\mathrm{test}\:\mathrm{them}\right) \\ $$$${r}=\frac{\mathrm{3}}{\mathrm{8}}\vee{r}=\frac{\mathrm{6}−\mathrm{3}\sqrt{\mathrm{2}}}{\mathrm{4}} \\ $$
Commented by ajfour last updated on 17/Nov/23
$${I}\:\:{get}\:\:\mathrm{8}{r}^{\mathrm{2}} −\mathrm{24}{r}+\mathrm{9}=\mathrm{0} \\ $$$$\Rightarrow\:\:{r}=\frac{\mathrm{3}}{\mathrm{4}}\left(\mathrm{2}\pm\sqrt{\mathrm{2}}\right) \\ $$$${but}\:{r}=\frac{\mathrm{3}}{\mathrm{4}}\left(\mathrm{2}−\sqrt{\mathrm{2}}\right)\:\:{can}\:{only}\:{be}\:{selected}. \\ $$
Commented by Frix last updated on 17/Nov/23
$$\mathrm{I}\:\mathrm{tested}\:\mathrm{my}\:\mathrm{solutions}\:\Rightarrow\:{r}=\frac{\mathrm{3}}{\mathrm{8}}\:\mathrm{is}\:\mathrm{wrong} \\ $$