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Question Number 190936 by Spillover last updated on 14/Apr/23

$$\mathrm{Determine}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{such}\mathrm{that}$$$${\mathrm{e}}^{\sinh {}^{-1}\mathrm{x}}=1+{\mathrm{e}}^{\cosh {}^{-1}\mathrm{x}}$$

Answered by mr W last updated on 14/Apr/23

$$x+\sqrt{x^2+1}=1+x+\sqrt{x^2-1}$$$$\sqrt{x^2+1}=1+\sqrt{x^2-1}$$$$x^2+1=1+x^2-1+2\sqrt{x^2-1}$$$$\sqrt{x^2-1}=\frac{1}{2}$$$$x^2-1=\frac{1}{4}$$$$x=\pm \frac{\sqrt{5}}{2}✓$$

Commented by Spillover last updated on 15/Apr/23

$$thankyou$$

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