Question Number 123587 by ajfour last updated on 26/Nov/20
Commented by ajfour last updated on 26/Nov/20
$${Find}\:{x}\:{in}\:{terms}\:{of}\:{c}.\: \\ $$
Answered by ajfour last updated on 01/Dec/20
$$\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\left(\mathrm{1}+\frac{{c}}{{x}}\:\right)\sqrt{{c}^{\mathrm{2}} +\mathrm{4}}=\:\mathrm{2}{x}+{c}\left(\mathrm{2}+\frac{{c}}{{x}}\right) \\ $$$$\Rightarrow \\ $$$$\sqrt{{x}+\frac{\mathrm{1}}{{x}}}\:\left({c}+{x}\right)\sqrt{{c}^{\mathrm{2}} +\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\mathrm{2}{x}+\frac{{c}^{\mathrm{2}} }{{x}}\right)+\mathrm{2}{c} \\ $$$$..... \\ $$