Roots of hyperbolic functions I am having difficulty with

Caerswso1pc

Caerswso1pc

Answered question

2022-04-02

Roots of hyperbolic functions
I am having difficulty with understanding one part of the answer to the following:
Find conditions on a, b, and c which are necessary and sufficient to ensure that the equations
acoshx+bsinhx=c
has exactly one root.

Answer & Explanation

Alexzander Evans

Alexzander Evans

Beginner2022-04-03Added 9 answers

If you let ex=y, you end with the equation
(a+b)y22cy+(ab)=0
So, first we need two roots Δ=b2+c2a20
and one of them must be negative since y>0 so aba+b<0
that is to say a2b2<0.

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