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6x/(2x^2-10x+5)+5x/(2x^2-6x+5)>=3

6x/(2x^2-10x+5)+5x/(2x^2-6x+5)>=3 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
      6*x              5*x           
--------------- + -------------- >= 3
   2                 2               
2*x  - 10*x + 5   2*x  - 6*x + 5     
$$\frac{5 x}{\left(2 x^{2} - 6 x\right) + 5} + \frac{6 x}{\left(2 x^{2} - 10 x\right) + 5} \geq 3$$
(5*x)/(2*x^2 - 6*x + 5) + (6*x)/(2*x^2 - 10*x + 5) >= 3
Respuesta rápida 2 [src]
        _____        ____                      ____         _____ 
 19   \/ 271   5   \/ 15                 5   \/ 15   19   \/ 271  
[-- - -------, - - ------) U [1, 5/2] U (- + ------, -- + -------]
 6       6     2     2                   2     2     6       6    
$$x\ in\ \left[\frac{19}{6} - \frac{\sqrt{271}}{6}, \frac{5}{2} - \frac{\sqrt{15}}{2}\right) \cup \left[1, \frac{5}{2}\right] \cup \left(\frac{\sqrt{15}}{2} + \frac{5}{2}, \frac{\sqrt{271}}{6} + \frac{19}{6}\right]$$
x in Union(Interval(1, 5/2), Interval.Ropen(19/6 - sqrt(271)/6, 5/2 - sqrt(15)/2), Interval.Lopen(sqrt(15)/2 + 5/2, sqrt(271)/6 + 19/6))
Respuesta rápida [src]
  /                          /            _____        ____    \     /       _____                 ____\\
  |                          |     19   \/ 271   5   \/ 15     |     |19   \/ 271            5   \/ 15 ||
Or|And(1 <= x, x <= 5/2), And|x <= -- + -------, - + ------ < x|, And|-- - ------- <= x, x < - - ------||
  \                          \     6       6     2     2       /     \6       6              2     2   //
$$\left(1 \leq x \wedge x \leq \frac{5}{2}\right) \vee \left(x \leq \frac{\sqrt{271}}{6} + \frac{19}{6} \wedge \frac{\sqrt{15}}{2} + \frac{5}{2} < x\right) \vee \left(\frac{19}{6} - \frac{\sqrt{271}}{6} \leq x \wedge x < \frac{5}{2} - \frac{\sqrt{15}}{2}\right)$$
((1 <= x)∧(x <= 5/2))∨((x <= 19/6 + sqrt(271)/6)∧(5/2 + sqrt(15)/2 < x))∨((19/6 - sqrt(271)/6 <= x)∧(x < 5/2 - sqrt(15)/2))
Gráfico
6x/(2x^2-10x+5)+5x/(2x^2-6x+5)>=3 desigualdades