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2^sqrt(x)+1-2^(sqrt(x)+1)-2^(sqrt(x)-1)=12 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   ___          ___          ___         
 \/ x         \/ x  + 1    \/ x  - 1     
2      + 1 - 2          - 2          = 12
−2x−1+(−2x+1+(2x+1))=12- 2^{\sqrt{x} - 1} + \left(- 2^{\sqrt{x} + 1} + \left(2^{\sqrt{x}} + 1\right)\right) = 12
Simplificar
Gráfica
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.515.010.012.5-2525
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
        2           2                   
     log (22/3) - pi    2*pi*I*log(22/3)
x1 = ---------------- + ----------------
            2                  2        
         log (2)            log (2)
x1=−π2+log⁡(223)2log⁡(2)2+2iπlog⁡(223)log⁡(2)2x_{1} = \frac{- \pi^{2} + \log{\left(\frac{22}{3} \right)}^{2}}{\log{\left(2 \right)}^{2}} + \frac{2 i \pi \log{\left(\frac{22}{3} \right)}}{\log{\left(2 \right)}^{2}} 
x1 = (-pi^2 + log(22/3)^2)/log(2)^2 + 2*i*pi*log(22/3)/log(2)^2
Suma y producto de raíces [src] 
suma
   2           2                   
log (22/3) - pi    2*pi*I*log(22/3)
---------------- + ----------------
       2                  2        
    log (2)            log (2)
−π2+log⁡(223)2log⁡(2)2+2iπlog⁡(223)log⁡(2)2\frac{- \pi^{2} + \log{\left(\frac{22}{3} \right)}^{2}}{\log{\left(2 \right)}^{2}} + \frac{2 i \pi \log{\left(\frac{22}{3} \right)}}{\log{\left(2 \right)}^{2}} 
=
   2           2                   
log (22/3) - pi    2*pi*I*log(22/3)
---------------- + ----------------
       2                  2        
    log (2)            log (2)
−π2+log⁡(223)2log⁡(2)2+2iπlog⁡(223)log⁡(2)2\frac{- \pi^{2} + \log{\left(\frac{22}{3} \right)}^{2}}{\log{\left(2 \right)}^{2}} + \frac{2 i \pi \log{\left(\frac{22}{3} \right)}}{\log{\left(2 \right)}^{2}} 
producto
   2           2                   
log (22/3) - pi    2*pi*I*log(22/3)
---------------- + ----------------
       2                  2        
    log (2)            log (2)
−π2+log⁡(223)2log⁡(2)2+2iπlog⁡(223)log⁡(2)2\frac{- \pi^{2} + \log{\left(\frac{22}{3} \right)}^{2}}{\log{\left(2 \right)}^{2}} + \frac{2 i \pi \log{\left(\frac{22}{3} \right)}}{\log{\left(2 \right)}^{2}} 
=
   2           2        /    2*pi\
log (22/3) - pi  + I*log\22/3    /
----------------------------------
                2                 
             log (2)
−π2+log⁡(223)2+ilog⁡((223)2π)log⁡(2)2\frac{- \pi^{2} + \log{\left(\frac{22}{3} \right)}^{2} + i \log{\left(\left(\frac{22}{3}\right)^{2 \pi} \right)}}{\log{\left(2 \right)}^{2}} 
(log(22/3)^2 - pi^2 + i*log((22/3)^(2*pi)))/log(2)^2
Respuesta numérica [src] 
x1 = -505.294638670742 - 130.281292589563*i
x2 = -12.2797157453702 - 26.0562585179126*i
x3 = -12.2797157453702 + 26.0562585179126*i
x4 = -176.618023387161 - 78.1687755537377*i
x5 = -176.618023387161 + 78.1687755537377*i
x5 = -176.618023387161 + 78.1687755537377*i
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