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acos(2^x-2^-x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
    / x    -x\    
acos\2  - 2  / = 0
acos⁡(2x−2−x)=0\operatorname{acos}{\left(2^{x} - 2^{- x} \right)} = 0
Simplificar
Gráfica
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.005
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                         /        ___\         
                         |  1   \/ 5 |         
        /      ___\   log|- - + -----|         
     log\1 + \/ 5 /      \  2     2  /    pi*I 
-1 + -------------- + ---------------- + ------
         log(2)            log(2)        log(2)
(−1+log⁡(1+5)log⁡(2))+(log⁡(−12+52)log⁡(2)+iπlog⁡(2))\left(-1 + \frac{\log{\left(1 + \sqrt{5} \right)}}{\log{\left(2 \right)}}\right) + \left(\frac{\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}\right) 
=
                         /        ___\         
                         |  1   \/ 5 |         
        /      ___\   log|- - + -----|         
     log\1 + \/ 5 /      \  2     2  /    pi*I 
-1 + -------------- + ---------------- + ------
         log(2)            log(2)        log(2)
−1+log⁡(−12+52)log⁡(2)+log⁡(1+5)log⁡(2)+iπlog⁡(2)-1 + \frac{\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(1 + \sqrt{5} \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}} 
producto
                      /   /        ___\         \
                      |   |  1   \/ 5 |         |
/        /      ___\\ |log|- - + -----|         |
|     log\1 + \/ 5 /| |   \  2     2  /    pi*I |
|-1 + --------------|*|---------------- + ------|
\         log(2)    / \     log(2)        log(2)/
(−1+log⁡(1+5)log⁡(2))(log⁡(−12+52)log⁡(2)+iπlog⁡(2))\left(-1 + \frac{\log{\left(1 + \sqrt{5} \right)}}{\log{\left(2 \right)}}\right) \left(\frac{\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}\right) 
=
                              /              1   \
                              |           -------|
                              |              2   |
 /          /        ___\\    |           log (2)|
 |          |  1   \/ 5 ||    |/    2    \       |
-|pi*I + log|- - + -----||*log||---------|       |
 \          \  2     2  //    ||      ___|       |
                              \\1 + \/ 5 /       /
−(log⁡(−12+52)+iπ)log⁡((21+5)1log⁡(2)2)- \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right) \log{\left(\left(\frac{2}{1 + \sqrt{5}}\right)^{\frac{1}{\log{\left(2 \right)}^{2}}} \right)} 
-(pi*i + log(-1/2 + sqrt(5)/2))*log((2/(1 + sqrt(5)))^(log(2)^(-2)))
Respuesta rápida [src] 
             /      ___\
          log\1 + \/ 5 /
x1 = -1 + --------------
              log(2)
x1=−1+log⁡(1+5)log⁡(2)x_{1} = -1 + \frac{\log{\left(1 + \sqrt{5} \right)}}{\log{\left(2 \right)}} 
        /        ___\         
        |  1   \/ 5 |         
     log|- - + -----|         
        \  2     2  /    pi*I 
x2 = ---------------- + ------
          log(2)        log(2)
x2=log⁡(−12+52)log⁡(2)+iπlog⁡(2)x_{2} = \frac{\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}} 
x2 = log(-1/2 + sqrt(5)/2)/log(2) + i*pi/log(2)
Respuesta numérica [src] 
x1 = -0.694241913630617 + 4.53236014182719*i
x2 = 0.694241913630617
x2 = 0.694241913630617
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