Question

How do you solve `13 sinh x - 7 cosh x+1=0`?

Answer 1

x = 0.5108, nearly.

Explanation:

Using `sinh x =(e^x-e^(-x))/2 and cosh x = (e^x+e^(-x))/2`,

the given equation reduces to

`3 e^(2x)+e^x-10=0`. Solving this quadratic in `e^x`,

`e^x=-2 and 5/3`..

As #e^x>0, e^x = 5/3..

Inversely, `x = ln (5/3)=0.51082563`, nearly.