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sqrt(3x+1)>sqrt^3(13x-1) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
                          3
  _________     __________ 
\/ 3*x + 1  > \/ 13*x - 1  
$$\sqrt{3 x + 1} > \left(\sqrt{13 x - 1}\right)^{3}$$
sqrt(3*x + 1) > (sqrt(13*x - 1))^3
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
   /                              _________________                           \
   |                    3 ____ 3 /         _______               2/3          |
   |               1    \/ 13 *\/  104 + \/ 10803              13             |
And|1/13 <= x, x < -- + --------------------------- + ------------------------|
   |               13               169                      _________________|
   |                                                      3 /         _______ |
   \                                                  169*\/  104 + \/ 10803  /
$$\frac{1}{13} \leq x \wedge x < \frac{13^{\frac{2}{3}}}{169 \sqrt[3]{\sqrt{10803} + 104}} + \frac{1}{13} + \frac{\sqrt[3]{13} \sqrt[3]{\sqrt{10803} + 104}}{169}$$
(1/13 <= x)∧(x < 1/13 + 13^(1/3)*(104 + sqrt(10803))^(1/3)/169 + 13^(2/3)/(169*(104 + sqrt(10803))^(1/3)))
Respuesta rápida 2 [src]
                      _________________                            
            3 ____ 3 /         _______               2/3           
       1    \/ 13 *\/  104 + \/ 10803              13              
[1/13, -- + --------------------------- + ------------------------)
       13               169                      _________________ 
                                              3 /         _______  
                                          169*\/  104 + \/ 10803   
$$x\ in\ \left[\frac{1}{13}, \frac{13^{\frac{2}{3}}}{169 \sqrt[3]{\sqrt{10803} + 104}} + \frac{1}{13} + \frac{\sqrt[3]{13} \sqrt[3]{\sqrt{10803} + 104}}{169}\right)$$
x in Interval.Ropen(1/13, 13^(2/3)/(169*(sqrt(10803) + 104)^(1/3)) + 1/13 + 13^(1/3)*(sqrt(10803) + 104)^(1/3)/169)