Solve-for-x-e-sinh-1-x-1-e-cosh-1-x-

Question Number 178575 by Spillover last updated on 18/Oct/22

Solve for x

e^{\sinh^{- 1} x} = 1 + e^{\cosh^{- 1} x}

Answered by mr W last updated on 19/Oct/22

x + \sqrt{x^{2} + 1} = 1 + x + \sqrt{x^{2} - 1}

\sqrt{x^{2} + 1} = 1 + \sqrt{x^{2} - 1}

x^{2} + 1 = x^{2} + 2 \sqrt{x^{2} - 1}

1 = 2 \sqrt{x^{2} - 1}

x^{2} - 1 = \frac{1}{4}

\Rightarrow x = \pm \frac{\sqrt{5}}{2}

Commented by Spillover last updated on 19/Oct/22

thanks