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((x^2-9)*sqrt(2-x))/2*x+3>=0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
/ 2    \   _______           
\x  - 9/*\/ 2 - x            
------------------*x + 3 >= 0
        2                    
$$x \frac{\sqrt{2 - x} \left(x^{2} - 9\right)}{2} + 3 \geq 0$$
x*((sqrt(2 - x)*(x^2 - 9))/2) + 3 >= 0
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
  /   /               / 7      6       5       4       3        2        \     \     /            / 7      6       5       4       3        2        \         / 7      6       5       4       3        2        \     \\
Or\And\x <= 2, CRootOf\x  - 2*x  - 18*x  + 36*x  + 81*x  - 162*x  + 36, 4/ <= x/, And\x <= CRootOf\x  - 2*x  - 18*x  + 36*x  + 81*x  - 162*x  + 36, 3/, CRootOf\x  - 2*x  - 18*x  + 36*x  + 81*x  - 162*x  + 36, 0/ <= x//
$$\left(x \leq 2 \wedge \operatorname{CRootOf} {\left(x^{7} - 2 x^{6} - 18 x^{5} + 36 x^{4} + 81 x^{3} - 162 x^{2} + 36, 4\right)} \leq x\right) \vee \left(x \leq \operatorname{CRootOf} {\left(x^{7} - 2 x^{6} - 18 x^{5} + 36 x^{4} + 81 x^{3} - 162 x^{2} + 36, 3\right)} \wedge \operatorname{CRootOf} {\left(x^{7} - 2 x^{6} - 18 x^{5} + 36 x^{4} + 81 x^{3} - 162 x^{2} + 36, 0\right)} \leq x\right)$$
((x <= 2)∧(CRootOf(x^7 - 2*x^6 - 18*x^5 + 36*x^4 + 81*x^3 - 162*x^2 + 36, 4) <= x))∨((x <= CRootOf(x^7 - 2*x^6 - 18*x^5 + 36*x^4 + 81*x^3 - 162*x^2 + 36, 3))∧(CRootOf(x^7 - 2*x^6 - 18*x^5 + 36*x^4 + 81*x^3 - 162*x^2 + 36, 0) <= x))
Respuesta rápida 2 [src]
        / 7      6       5       4       3        2        \         / 7      6       5       4       3        2        \            / 7      6       5       4       3        2        \    
[CRootOf\x  - 2*x  - 18*x  + 36*x  + 81*x  - 162*x  + 36, 0/, CRootOf\x  - 2*x  - 18*x  + 36*x  + 81*x  - 162*x  + 36, 3/] U [CRootOf\x  - 2*x  - 18*x  + 36*x  + 81*x  - 162*x  + 36, 4/, 2]
$$x\ in\ \left[\operatorname{CRootOf} {\left(x^{7} - 2 x^{6} - 18 x^{5} + 36 x^{4} + 81 x^{3} - 162 x^{2} + 36, 0\right)}, \operatorname{CRootOf} {\left(x^{7} - 2 x^{6} - 18 x^{5} + 36 x^{4} + 81 x^{3} - 162 x^{2} + 36, 3\right)}\right] \cup \left[\operatorname{CRootOf} {\left(x^{7} - 2 x^{6} - 18 x^{5} + 36 x^{4} + 81 x^{3} - 162 x^{2} + 36, 4\right)}, 2\right]$$
x in Union(Interval(CRootOf(x^7 - 2*x^6 - 18*x^5 + 36*x^4 + 81*x^3 - 162*x^2 + 36, 0), CRootOf(x^7 - 2*x^6 - 18*x^5 + 36*x^4 + 81*x^3 - 162*x^2 + 36, 3)), Interval(CRootOf(x^7 - 2*x^6 - 18*x^5 + 36*x^4 + 81*x^3 - 162*x^2 + 36, 4), 2))