Determine-the-value-of-x-such-that-e-sinh-1-x-1-e-cosh-1-x-

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

Determine the value of x such that

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

t h a n k y o u