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Resolver desigualdades/ sqrt5x-x^2>x-2

sqrt5x-x^2>x-2 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
  _____    2        
\/ 5*x  - x  > x - 2
−x2+5x>x−2- x^{2} + \sqrt{5 x} > x - 2 
-x^2 + sqrt(5*x) > x - 2
Solución de la desigualdad en el gráfico
01234567-5-4-3-2-1-5050
Respuesta rápida [src] 
   /                                                                                                                ____________________________________________________________________________________________________________________________________\
   |                                                                                                               /                ___________________            3 ____                                             ___                               |
   |                                                                                                 ___          /       3 ____ 3 /           _______          74*\/ 18                                         60*\/ 6                                |
   |                                                                                               \/ 6 *        /   36 - \/ 12 *\/  981 + 5*\/ 14181   - ---------------------- + -------------------------------------------------------------------- |
   |                               _____________________________________________________________                /                                            ___________________          _____________________________________________________________ |
   |                              /                ___________________            3 ____                       /                                          3 /           _______          /                ___________________            3 ____         |
   |                    ___      /       3 ____ 3 /           _______          74*\/ 18                       /                                           \/  981 + 5*\/ 14181          /       3 ____ 3 /           _______          74*\/ 18          |
   |                  \/ 6 *    /   18 + \/ 12 *\/  981 + 5*\/ 14181   + ----------------------              /                                                                         /   18 + \/ 12 *\/  981 + 5*\/ 14181   + ----------------------  |
   |                           /                                            ___________________             /                                                                         /                                            ___________________  |
   |                          /                                          3 /           _______             /                                                                         /                                          3 /           _______   |
   |              1         \/                                           \/  981 + 5*\/ 14181            \/                                                                        \/                                           \/  981 + 5*\/ 14181    |
And|0 <= x, x < - - + -------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------|
   \              2                                       12                                                                                                                 12                                                                         /
0≤x∧x<−12+6−123514181+9813−74183514181+9813+60674183514181+9813+18+123514181+9813+3612+674183514181+9813+18+123514181+9813120 \leq x \wedge x < - \frac{1}{2} + \frac{\sqrt{6} \sqrt{- \sqrt[3]{12} \sqrt[3]{5 \sqrt{14181} + 981} - \frac{74 \sqrt[3]{18}}{\sqrt[3]{5 \sqrt{14181} + 981}} + \frac{60 \sqrt{6}}{\sqrt{\frac{74 \sqrt[3]{18}}{\sqrt[3]{5 \sqrt{14181} + 981}} + 18 + \sqrt[3]{12} \sqrt[3]{5 \sqrt{14181} + 981}}} + 36}}{12} + \frac{\sqrt{6} \sqrt{\frac{74 \sqrt[3]{18}}{\sqrt[3]{5 \sqrt{14181} + 981}} + 18 + \sqrt[3]{12} \sqrt[3]{5 \sqrt{14181} + 981}}}{12} 
(0 <= x)∧(x < -1/2 + sqrt(6)*sqrt(18 + 12^(1/3)*(981 + 5*sqrt(14181))^(1/3) + 74*18^(1/3)/(981 + 5*sqrt(14181))^(1/3))/12 + sqrt(6)*sqrt(36 - 12^(1/3)*(981 + 5*sqrt(14181))^(1/3) - 74*18^(1/3)/(981 + 5*sqrt(14181))^(1/3) + 60*sqrt(6)/sqrt(18 + 12^(1/3)*(981 + 5*sqrt(14181))^(1/3) + 74*18^(1/3)/(981 + 5*sqrt(14181))^(1/3)))/12)
Respuesta rápida 2 [src] 
                                                                                                        ____________________________________________________________________________________________________________________________________ 
                                                                                                       /                ___________________            3 ____                                             ___                                
                                                                                         ___          /       3 ____ 3 /           _______          74*\/ 18                                         60*\/ 6                                 
                                                                                       \/ 6 *        /   36 - \/ 12 *\/  981 + 5*\/ 14181   - ---------------------- + --------------------------------------------------------------------  
                       _____________________________________________________________                /                                            ___________________          _____________________________________________________________  
                      /                ___________________            3 ____                       /                                          3 /           _______          /                ___________________            3 ____          
            ___      /       3 ____ 3 /           _______          74*\/ 18                       /                                           \/  981 + 5*\/ 14181          /       3 ____ 3 /           _______          74*\/ 18           
          \/ 6 *    /   18 + \/ 12 *\/  981 + 5*\/ 14181   + ----------------------              /                                                                         /   18 + \/ 12 *\/  981 + 5*\/ 14181   + ----------------------   
                   /                                            ___________________             /                                                                         /                                            ___________________   
                  /                                          3 /           _______             /                                                                         /                                          3 /           _______    
      1         \/                                           \/  981 + 5*\/ 14181            \/                                                                        \/                                           \/  981 + 5*\/ 14181     
[0, - - + -------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------)
      2                                       12                                                                                                                 12
x in [0,−12+6−123514181+9813−74183514181+9813+60674183514181+9813+18+123514181+9813+3612+674183514181+9813+18+123514181+981312)x\ in\ \left[0, - \frac{1}{2} + \frac{\sqrt{6} \sqrt{- \sqrt[3]{12} \sqrt[3]{5 \sqrt{14181} + 981} - \frac{74 \sqrt[3]{18}}{\sqrt[3]{5 \sqrt{14181} + 981}} + \frac{60 \sqrt{6}}{\sqrt{\frac{74 \sqrt[3]{18}}{\sqrt[3]{5 \sqrt{14181} + 981}} + 18 + \sqrt[3]{12} \sqrt[3]{5 \sqrt{14181} + 981}}} + 36}}{12} + \frac{\sqrt{6} \sqrt{\frac{74 \sqrt[3]{18}}{\sqrt[3]{5 \sqrt{14181} + 981}} + 18 + \sqrt[3]{12} \sqrt[3]{5 \sqrt{14181} + 981}}}{12}\right) 
x in Interval.Ropen(0, -1/2 + sqrt(6)*sqrt(-12^(1/3)*(5*sqrt(14181) + 981)^(1/3) - 74*18^(1/3)/(5*sqrt(14181) + 981)^(1/3) + 60*sqrt(6)/sqrt(74*18^(1/3)/(5*sqrt(14181) + 981)^(1/3) + 18 + 12^(1/3)*(5*sqrt(14181) + 981)^(1/3)) + 36)/12 + sqrt(6)*sqrt(74*18^(1/3)/(5*sqrt(14181) + 981)^(1/3) + 18 + 12^(1/3)*(5*sqrt(14181) + 981)^(1/3))/12)
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