Sr Examen

Otras calculadoras


4/(2x+1)^2+3/(2x+5)^2>7/(2x+5)(2x+1)

4/(2x+1)^2+3/(2x+5)^2>7/(2x+5)(2x+1) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
    4            3           7             
---------- + ---------- > -------*(2*x + 1)
         2            2   2*x + 5          
(2*x + 1)    (2*x + 5)                     
$$\frac{3}{\left(2 x + 5\right)^{2}} + \frac{4}{\left(2 x + 1\right)^{2}} > \left(2 x + 1\right) \frac{7}{2 x + 5}$$
3/(2*x + 5)^2 + 4/(2*x + 1)^2 > (2*x + 1)*(7/(2*x + 5))
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
  /                            /                     /    4        3        2               \\     /                 /    4        3        2               \    \\
Or\And(-5/2 < x, x < -1/2), And\-1/2 < x, x < CRootOf\28*x  + 112*x  + 119*x  + 33*x - 17, 1//, And\x < -5/2, CRootOf\28*x  + 112*x  + 119*x  + 33*x - 17, 0/ < x//
$$\left(- \frac{5}{2} < x \wedge x < - \frac{1}{2}\right) \vee \left(- \frac{1}{2} < x \wedge x < \operatorname{CRootOf} {\left(28 x^{4} + 112 x^{3} + 119 x^{2} + 33 x - 17, 1\right)}\right) \vee \left(x < - \frac{5}{2} \wedge \operatorname{CRootOf} {\left(28 x^{4} + 112 x^{3} + 119 x^{2} + 33 x - 17, 0\right)} < x\right)$$
((-5/2 < x)∧(x < -1/2))∨((-1/2 < x)∧(x < CRootOf(28*x^4 + 112*x^3 + 119*x^2 + 33*x - 17, 1)))∨((x < -5/2)∧(CRootOf(28*x^4 + 112*x^3 + 119*x^2 + 33*x - 17, 0) < x))
Respuesta rápida 2 [src]
        /    4        3        2               \                                       /    4        3        2               \ 
(CRootOf\28*x  + 112*x  + 119*x  + 33*x - 17, 0/, -5/2) U (-5/2, -1/2) U (-1/2, CRootOf\28*x  + 112*x  + 119*x  + 33*x - 17, 1/)
$$x\ in\ \left(\operatorname{CRootOf} {\left(28 x^{4} + 112 x^{3} + 119 x^{2} + 33 x - 17, 0\right)}, - \frac{5}{2}\right) \cup \left(- \frac{5}{2}, - \frac{1}{2}\right) \cup \left(- \frac{1}{2}, \operatorname{CRootOf} {\left(28 x^{4} + 112 x^{3} + 119 x^{2} + 33 x - 17, 1\right)}\right)$$
x in Union(Interval.open(-5/2, -1/2), Interval.open(-1/2, CRootOf(28*x^4 + 112*x^3 + 119*x^2 + 33*x - 17, 1)), Interval.open(CRootOf(28*x^4 + 112*x^3 + 119*x^2 + 33*x - 17, 0), -5/2))
Gráfico
4/(2x+1)^2+3/(2x+5)^2>7/(2x+5)(2x+1) desigualdades