Question Number 183795 by AROUNAMoussa last updated on 30/Dec/22
Answered by HeferH last updated on 30/Dec/22
$$\:\left({a}+{b}\right)^{\mathrm{2}} −\left({a}−{b}\right)^{\mathrm{2}} =\:\mathrm{4}{ab}\:\Rightarrow \\ $$$$\:\sqrt{\left(\mathrm{325}\right)^{\mathrm{2}} −\left(\mathrm{125}\right)^{\mathrm{2}} }\:=\:\sqrt{\mathrm{400}{r}}\:+\:\sqrt{\mathrm{4}\centerdot\mathrm{225}\centerdot{r}} \\ $$$$\:\sqrt{\mathrm{450}\centerdot\mathrm{200}}=\:\mathrm{20}\sqrt{{r}}\:+\:\mathrm{30}\sqrt{{r}} \\ $$$$\:\sqrt{\mathrm{450}\centerdot\mathrm{200}}=\:\mathrm{50}\sqrt{{r}} \\ $$$$\:\frac{\mathrm{450}\centerdot\mathrm{200}}{\mathrm{2500}}\:={r}\:=\:\frac{\mathrm{45}\centerdot\mathrm{20}}{\mathrm{25}}=\:\:\mathrm{36}{u} \\ $$
Answered by cortano1 last updated on 30/Dec/22
$$\:\frac{\mathrm{1}}{\:\sqrt{{r}}}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{225}}}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{100}}} \\ $$$$\:\frac{\mathrm{1}}{\:\sqrt{{r}}}\:=\:\frac{\mathrm{1}}{\mathrm{15}}+\frac{\mathrm{1}}{\mathrm{10}}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\Rightarrow\:{r}=\:\mathrm{6}^{\mathrm{2}} =\:\mathrm{36}\: \\ $$