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Question-186165




Question Number 186165 by ajfour last updated on 01/Feb/23
Answered by mr W last updated on 01/Feb/23
(c/x)=((x−1)/( (√(x^2 −(x−1)^2 ))))=((x−1)/( (√(2x−1))))  x(x−1)=c(√(2x−1))  x^4 −2x^3 +x^2 −2c^2 x+c^2 =0  ...
$$\frac{{c}}{{x}}=\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\left({x}−\mathrm{1}\right)^{\mathrm{2}} }}=\frac{{x}−\mathrm{1}}{\:\sqrt{\mathrm{2}{x}−\mathrm{1}}} \\ $$$${x}\left({x}−\mathrm{1}\right)={c}\sqrt{\mathrm{2}{x}−\mathrm{1}} \\ $$$${x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{2}{c}^{\mathrm{2}} {x}+{c}^{\mathrm{2}} =\mathrm{0} \\ $$$$… \\ $$

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