Sr Examen

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