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Resolver desigualdades/ -x/(1-x)+(sqrt(2)*x)^2<=8*x^2-5+1/x

-x/(1-x)+(sqrt(2)*x)^2<=8*x^2-5+1/x desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
                 2                
 -x     /  ___  \        2       1
----- + \\/ 2 *x/  <= 8*x  - 5 + -
1 - x                            x
(−1)x1−x+(2x)2≤(8x2−5)+1x\frac{\left(-1\right) x}{1 - x} + \left(\sqrt{2} x\right)^{2} \leq \left(8 x^{2} - 5\right) + \frac{1}{x} 
(-x)/(1 - x) + (sqrt(2)*x)^2 <= 8*x^2 - 5 + 1/x
Solución de la desigualdad en el gráfico
05-20-15-10-5101520-50005000
Respuesta rápida [src] 
  /   /            /   4      3      2             \         \     /            /   4      3      2             \       \     /       /   4      3      2             \            \     /       /   4      3      2             \             \\
Or\And\x <= CRootOf\6*x  - 6*x  - 6*x  + 6*x - 1, 0/, -oo < x/, And\x <= CRootOf\6*x  - 6*x  - 6*x  + 6*x - 1, 1/, 0 < x/, And\CRootOf\6*x  - 6*x  - 6*x  + 6*x - 1, 2/ <= x, x < 1/, And\CRootOf\6*x  - 6*x  - 6*x  + 6*x - 1, 3/ <= x, x < oo//
(x≤CRootOf⁡(6x4−6x3−6x2+6x−1,0)∧−∞<x)∨(x≤CRootOf⁡(6x4−6x3−6x2+6x−1,1)∧0<x)∨(CRootOf⁡(6x4−6x3−6x2+6x−1,2)≤x∧x<1)∨(CRootOf⁡(6x4−6x3−6x2+6x−1,3)≤x∧x<∞)\left(x \leq \operatorname{CRootOf} {\left(6 x^{4} - 6 x^{3} - 6 x^{2} + 6 x - 1, 0\right)} \wedge -\infty < x\right) \vee \left(x \leq \operatorname{CRootOf} {\left(6 x^{4} - 6 x^{3} - 6 x^{2} + 6 x - 1, 1\right)} \wedge 0 < x\right) \vee \left(\operatorname{CRootOf} {\left(6 x^{4} - 6 x^{3} - 6 x^{2} + 6 x - 1, 2\right)} \leq x \wedge x < 1\right) \vee \left(\operatorname{CRootOf} {\left(6 x^{4} - 6 x^{3} - 6 x^{2} + 6 x - 1, 3\right)} \leq x \wedge x < \infty\right) 
((-oo < x)∧(x <= CRootOf(6*x^4 - 6*x^3 - 6*x^2 + 6*x - 1, 0)))∨((0 < x)∧(x <= CRootOf(6*x^4 - 6*x^3 - 6*x^2 + 6*x - 1, 1)))∨((x < 1)∧(CRootOf(6*x^4 - 6*x^3 - 6*x^2 + 6*x - 1, 2) <= x))∨((x < oo)∧(CRootOf(6*x^4 - 6*x^3 - 6*x^2 + 6*x - 1, 3) <= x))
Respuesta rápida 2 [src] 
             /   4      3      2             \               /   4      3      2             \            /   4      3      2             \               /   4      3      2             \     
(-oo, CRootOf\6*x  - 6*x  - 6*x  + 6*x - 1, 0/] U (0, CRootOf\6*x  - 6*x  - 6*x  + 6*x - 1, 1/] U [CRootOf\6*x  - 6*x  - 6*x  + 6*x - 1, 2/, 1) U [CRootOf\6*x  - 6*x  - 6*x  + 6*x - 1, 3/, oo)
x in (−∞,CRootOf⁡(6x4−6x3−6x2+6x−1,0)]∪(0,CRootOf⁡(6x4−6x3−6x2+6x−1,1)]∪[CRootOf⁡(6x4−6x3−6x2+6x−1,2),1)∪[CRootOf⁡(6x4−6x3−6x2+6x−1,3),∞)x\ in\ \left(-\infty, \operatorname{CRootOf} {\left(6 x^{4} - 6 x^{3} - 6 x^{2} + 6 x - 1, 0\right)}\right] \cup \left(0, \operatorname{CRootOf} {\left(6 x^{4} - 6 x^{3} - 6 x^{2} + 6 x - 1, 1\right)}\right] \cup \left[\operatorname{CRootOf} {\left(6 x^{4} - 6 x^{3} - 6 x^{2} + 6 x - 1, 2\right)}, 1\right) \cup \left[\operatorname{CRootOf} {\left(6 x^{4} - 6 x^{3} - 6 x^{2} + 6 x - 1, 3\right)}, \infty\right) 
x in Union(Interval(-oo, CRootOf(6*x^4 - 6*x^3 - 6*x^2 + 6*x - 1, 0)), Interval.Lopen(0, CRootOf(6*x^4 - 6*x^3 - 6*x^2 + 6*x - 1, 1)), Interval.Ropen(CRootOf(6*x^4 - 6*x^3 - 6*x^2 + 6*x - 1, 2), 1), Interval(CRootOf(6*x^4 - 6*x^3 - 6*x^2 + 6*x - 1, 3), oo))
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