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((x-2)*(x-4)*(x-7))/(x+2)*(x+4)*(x+7)<1 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
(x - 2)*(x - 4)*(x - 7)                    
-----------------------*(x + 4)*(x + 7) < 1
         x + 2                             
$$\frac{\left(x - 4\right) \left(x - 2\right) \left(x - 7\right)}{x + 2} \left(x + 4\right) \left(x + 7\right) < 1$$
(((((x - 4)*(x - 2))*(x - 7))/(x + 2))*(x + 4))*(x + 7) < 1
Respuesta rápida [src]
  /   /                   / 5      4       3        2                  \\     /           / 5      4       3        2                  \         / 5      4       3        2                  \    \     /           / 5      4       3        2                  \         / 5      4       3        2                  \    \\
Or\And\-2 < x, x < CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 2//, And\x < CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 1/, CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 0/ < x/, And\x < CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 4/, CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 3/ < x//
$$\left(-2 < x \wedge x < \operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 2\right)}\right) \vee \left(x < \operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 1\right)} \wedge \operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 0\right)} < x\right) \vee \left(x < \operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 4\right)} \wedge \operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 3\right)} < x\right)$$
((-2 < x)∧(x < CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 2)))∨((x < CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 1))∧(CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 0) < x))∨((x < CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 4))∧(CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 3) < x))
Respuesta rápida 2 [src]
        / 5      4       3        2                  \         / 5      4       3        2                  \                / 5      4       3        2                  \            / 5      4       3        2                  \         / 5      4       3        2                  \ 
(CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 0/, CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 1/) U (-2, CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 2/) U (CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 3/, CRootOf\x  - 2*x  - 65*x  + 130*x  + 783*x - 1570, 4/)
$$x\ in\ \left(\operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 0\right)}, \operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 1\right)}\right) \cup \left(-2, \operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 2\right)}\right) \cup \left(\operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 3\right)}, \operatorname{CRootOf} {\left(x^{5} - 2 x^{4} - 65 x^{3} + 130 x^{2} + 783 x - 1570, 4\right)}\right)$$
x in Union(Interval.open(-2, CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 2)), Interval.open(CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 0), CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 1)), Interval.open(CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 3), CRootOf(x^5 - 2*x^4 - 65*x^3 + 130*x^2 + 783*x - 1570, 4)))