# Tagged Questions

Transcendental equations are equations containing transcendental functions, i.e. functions which are not algebraic. An algebraic function is a function that satisfies a polynomial equation whose terms are themselves polynomials with rational coefficients.

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### Find the number of solutions of $x^2+1=2^x$

I tried solving this equation $$x^2+1=2^x$$ but I was able to get only two roots , i.e. $x=0,1$ but the answer given said the equation has 3 roots when I looked at the graph given in the solution it ...
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### Are there any solutions to this equation?

I wonder how many there solutions to this equation? $$\left(\frac{w^2-1}{\left(w-1\right) w+1}\right){}^{\frac{1}{w}}=e$$
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### Find the roots of $e^x+e^{1/x} + a = 0$

Find the roots of this equation $e^x + e^{1/x} + a = 0$ where $a \in \Bbb R$ Is there any nice formula for this type of equation?
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### Please help me to solve the equation $e^{-\frac{x}{0.026}}=7.477 x^2 + 0.0146 x$ [closed]

This equation has $e^x$,$x^2$ and $x$ terms.So how can we solve this type of equation?
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### Solving for a $v$ in $\sum a_i e^{b_i (z^2+d_i) + c_i v}$

I have an equation in complex domain, $$P(e^u,e^v)=\sum_{i=1}^{N} a_i e^{b_i u + c_i v}=0 \;\;\;\text{(A)}$$ and by redefining, at the roots (I'm only showing work for one root), the first ...
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### Genus of trancendental curve

I understand that an algebraic curve is genus 0 iff it can be parameterized using rational functions. I am curious if there is a simple way to know if a transcendental curve is genus 0? Specifically ...
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### For what values of $x$ is $\cos x$ transcendental?

For what values of $x$ is $\cos x$ transcendental? Is there any way I can figure out the values of $x$ where $\cos x$ is transcendental or do I have to check individually for every $x$ whether it is ...
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### Difficulty in solving transcendental equation

Let $A,B,C$, and $D$ be positive constants. What's the most concise way to express $x$ in the equation below? $$A = B\arctan(x/C)+Dx,$$ where $0<x<1$ and we know that $C=\cos(30^\circ)$.
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### Find the positive root of the equation $\cosh x+\cos x-3=0$, other than numerically

I know you are able to find the root of the equation by using Newton-Raphson method. But is there any other way? $$\cosh x+\cos x-3=0$$ I thought maybe you could say that $-1\leq \cos x \leq 1$. So ...
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### Existence of solution for equation with erfc

I'm looking for the self-consistent (e.g. input needs to be the same as output) solution of $r$ in $$r = \frac{1}{2}\operatorname{erfc}(z(r))$$ where $\operatorname{erfc}$ is complimentary error ...