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Question Number 79423 by Rio Michael last updated on 25/Jan/20

$$solveforxandy$$$$sinhx-2coshy=0$$$$3coshx+6sihny=5$$

Answered by mr W last updated on 25/Jan/20

$$\cosh y=\frac{\sinh x}{2}...\left(i\right)$$$$\sinh y=\frac{5}{6}-\frac{\cosh x}{2}...\left(ii\right)$$$${\left(i\right)}^2-{\left(ii\right)}^2:$$$$1=\frac{{\sinh }^{2}x}{4}-\frac{25}{36}+\frac{5}{6}\cosh x-\frac{{\cosh }^{2}x}{4}$$$$1=-\frac{25}{36}+\frac{5}{6}\cosh x-1$$$$\Rightarrow \cosh x=\frac{97}{30}$$$$\Rightarrow x={\cosh }^{-1}\frac{97}{30}=\ln (\frac{97}{30}+\sqrt{{\left(\frac{97}{30}\right)}^2-1})=\ln \frac{97+\sqrt{8509}}{30}$$$$\sinh x=\pm \sqrt{{\left(\frac{97}{30}\right)}^2-1}=\pm \frac{\sqrt{8509}}{30}$$$$\cosh y=\frac{\sinh x}{2}=\pm \frac{\sqrt{8509}}{60}>1\Rightarrow only+$$$$\Rightarrow y={\cosh }^{-1}\frac{\sqrt{8509}}{60}=\ln \frac{\sqrt{4909}+\sqrt{8509}}{60}$$

Commented by Rio Michael last updated on 27/Jan/20

$$thankssir,seemslikehyperbolicfunctions{don}^{\prime }t$$$$suitsimultaneousequations$$

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