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(1.25(x+1)((2/x)+(((1.25^2)-1)/x^2)^0.5)-((1.25^2)-1))/(1+((1.25^2)/x^2))-20=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
          /          __________\                      
          |         /    2     |                      
5*(x + 1) |2       /  5/4  - 1 |        2             
---------*|- +    /   -------- | + - 5/4  + 1         
    4     |x     /        2    |                      
          \    \/        x     /                      
--------------------------------------------- - 20 = 0
                          2                           
                       5/4                            
                   1 + ----                           
                         2                            
                        x                             
$$-20 + \frac{\frac{5 \left(x + 1\right)}{4} \left(\sqrt{\frac{-1 + \left(\frac{5}{4}\right)^{2}}{x^{2}}} + \frac{2}{x}\right) + \left(1 - \left(\frac{5}{4}\right)^{2}\right)}{1 + \frac{\left(\frac{5}{4}\right)^{2}}{x^{2}}} = 0$$
Gráfica
Respuesta rápida [src]
                 _______
      55   5*I*\/ 21799 
x1 = --- - -------------
     548        548     
$$x_{1} = \frac{55}{548} - \frac{5 \sqrt{21799} i}{548}$$
                 _______
      55   5*I*\/ 21799 
x2 = --- + -------------
     548        548     
$$x_{2} = \frac{55}{548} + \frac{5 \sqrt{21799} i}{548}$$
x2 = 55/548 + 5*sqrt(21799)*i/548
Suma y producto de raíces [src]
suma
            _______               _______
 55   5*I*\/ 21799     55   5*I*\/ 21799 
--- - ------------- + --- + -------------
548        548        548        548     
$$\left(\frac{55}{548} - \frac{5 \sqrt{21799} i}{548}\right) + \left(\frac{55}{548} + \frac{5 \sqrt{21799} i}{548}\right)$$
=
 55
---
274
$$\frac{55}{274}$$
producto
/            _______\ /            _______\
| 55   5*I*\/ 21799 | | 55   5*I*\/ 21799 |
|--- - -------------|*|--- + -------------|
\548        548     / \548        548     /
$$\left(\frac{55}{548} - \frac{5 \sqrt{21799} i}{548}\right) \left(\frac{55}{548} + \frac{5 \sqrt{21799} i}{548}\right)$$
=
250
---
137
$$\frac{250}{137}$$
250/137
Respuesta numérica [src]
x1 = 0.10036496350365 - 1.34712449029371*i
x2 = 0.10036496350365 + 1.34712449029371*i
x2 = 0.10036496350365 + 1.34712449029371*i