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sqrt(1+1/(0.19*x)^2)*sqrt(1+1/(0.165*x)^2)=sqrt(2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
       _____________        _____________        
      /        1           /        1         ___
     /  1 + ------- *     /  1 + -------  = \/ 2 
    /             2      /             2         
   /        /19*x\      /        /33*x\          
  /         |----|     /         |----|          
\/          \100 /   \/          \200 /          
$$\sqrt{1 + \frac{1}{\left(\frac{33 x}{200}\right)^{2}}} \sqrt{1 + \frac{1}{\left(\frac{19 x}{100}\right)^{2}}} = \sqrt{2}$$
Gráfica
Respuesta rápida [src]
               _______________________
              /            __________ 
             /   2533    \/ 12706153  
x1 = -100*  /   ------ + ------------ 
          \/    786258      786258    
$$x_{1} = - 100 \sqrt{\frac{2533}{786258} + \frac{\sqrt{12706153}}{786258}}$$
              _______________________
             /            __________ 
            /   2533    \/ 12706153  
x2 = 100*  /   ------ + ------------ 
         \/    786258      786258    
$$x_{2} = 100 \sqrt{\frac{2533}{786258} + \frac{\sqrt{12706153}}{786258}}$$
x2 = 100*sqrt(2533/786258 + sqrt(12706153)/786258)
Suma y producto de raíces [src]
suma
           _______________________            _______________________
          /            __________            /            __________ 
         /   2533    \/ 12706153            /   2533    \/ 12706153  
- 100*  /   ------ + ------------  + 100*  /   ------ + ------------ 
      \/    786258      786258           \/    786258      786258    
$$- 100 \sqrt{\frac{2533}{786258} + \frac{\sqrt{12706153}}{786258}} + 100 \sqrt{\frac{2533}{786258} + \frac{\sqrt{12706153}}{786258}}$$
=
0
$$0$$
producto
          _______________________          _______________________
         /            __________          /            __________ 
        /   2533    \/ 12706153          /   2533    \/ 12706153  
-100*  /   ------ + ------------ *100*  /   ------ + ------------ 
     \/    786258      786258         \/    786258      786258    
$$- 100 \sqrt{\frac{2533}{786258} + \frac{\sqrt{12706153}}{786258}} \cdot 100 \sqrt{\frac{2533}{786258} + \frac{\sqrt{12706153}}{786258}}$$
=
                    __________
  12665000   5000*\/ 12706153 
- -------- - -----------------
   393129          393129     
$$- \frac{5000 \sqrt{12706153}}{393129} - \frac{12665000}{393129}$$
-12665000/393129 - 5000*sqrt(12706153)/393129
Respuesta numérica [src]
x1 = -8.80634767233756
x2 = 8.80634767233756
x2 = 8.80634767233756