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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.

$${Find}\:{x}\:{in}\:{terms}\:{of}\:{c}.\: \\ $$

Answered by ajfour last updated on 01/Dec/20

(√(1+x^2 )) (1+(c/x) )(√(c^2 +4))= 2x+c(2+(c/x))  ⇒  (√(x+(1/x))) (c+x)(√(c^2 +4))                    = (2x+(c^2 /x))+2c  .....

$$\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\left(\mathrm{1}+\frac{{c}}{{x}}\:\right)\sqrt{{c}^{\mathrm{2}} +\mathrm{4}}=\:\mathrm{2}{x}+{c}\left(\mathrm{2}+\frac{{c}}{{x}}\right) \\ $$$$\Rightarrow \\ $$$$\sqrt{{x}+\frac{\mathrm{1}}{{x}}}\:\left({c}+{x}\right)\sqrt{{c}^{\mathrm{2}} +\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\mathrm{2}{x}+\frac{{c}^{\mathrm{2}} }{{x}}\right)+\mathrm{2}{c} \\ $$$$..... \\ $$

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