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(2x^3-3x-1)^(1/2)=x-1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   ________________        
  /    3                   
\/  2*x  - 3*x - 1  = x - 1
$$\sqrt{\left(2 x^{3} - 3 x\right) - 1} = x - 1$$
Gráfica
Respuesta rápida [src]
              ________________                           
             /         ______                            
     1      /   59   \/ 1509                7            
x1 = - + 3 /   --- + --------  + ------------------------
     6   \/    108      72               ________________
                                        /         ______ 
                                       /   59   \/ 1509  
                                 36*3 /   --- + -------- 
                                    \/    108      72    
$$x_{1} = \frac{1}{6} + \frac{7}{36 \sqrt[3]{\frac{\sqrt{1509}}{72} + \frac{59}{108}}} + \sqrt[3]{\frac{\sqrt{1509}}{72} + \frac{59}{108}}$$
x1 = 1/6 + 7/(36*(sqrt(1509)/72 + 59/108)^(1/3)) + (sqrt(1509)/72 + 59/108)^(1/3)
Suma y producto de raíces [src]
suma
         ________________                           
        /         ______                            
1      /   59   \/ 1509                7            
- + 3 /   --- + --------  + ------------------------
6   \/    108      72               ________________
                                   /         ______ 
                                  /   59   \/ 1509  
                            36*3 /   --- + -------- 
                               \/    108      72    
$$\frac{1}{6} + \frac{7}{36 \sqrt[3]{\frac{\sqrt{1509}}{72} + \frac{59}{108}}} + \sqrt[3]{\frac{\sqrt{1509}}{72} + \frac{59}{108}}$$
=
         ________________                           
        /         ______                            
1      /   59   \/ 1509                7            
- + 3 /   --- + --------  + ------------------------
6   \/    108      72               ________________
                                   /         ______ 
                                  /   59   \/ 1509  
                            36*3 /   --- + -------- 
                               \/    108      72    
$$\frac{1}{6} + \frac{7}{36 \sqrt[3]{\frac{\sqrt{1509}}{72} + \frac{59}{108}}} + \sqrt[3]{\frac{\sqrt{1509}}{72} + \frac{59}{108}}$$
producto
         ________________                           
        /         ______                            
1      /   59   \/ 1509                7            
- + 3 /   --- + --------  + ------------------------
6   \/    108      72               ________________
                                   /         ______ 
                                  /   59   \/ 1509  
                            36*3 /   --- + -------- 
                               \/    108      72    
$$\frac{1}{6} + \frac{7}{36 \sqrt[3]{\frac{\sqrt{1509}}{72} + \frac{59}{108}}} + \sqrt[3]{\frac{\sqrt{1509}}{72} + \frac{59}{108}}$$
=
       __________________                          
    3 /           ______                           
1   \/  118 + 3*\/ 1509                7           
- + --------------------- + -----------------------
6             6                  __________________
                              3 /           ______ 
                            6*\/  118 + 3*\/ 1509  
$$\frac{1}{6} + \frac{7}{6 \sqrt[3]{3 \sqrt{1509} + 118}} + \frac{\sqrt[3]{3 \sqrt{1509} + 118}}{6}$$
1/6 + (118 + 3*sqrt(1509))^(1/3)/6 + 7/(6*(118 + 3*sqrt(1509))^(1/3))
Respuesta numérica [src]
x1 = 1.38367287043098
x1 = 1.38367287043098