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Otras calculadoras
- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
¿Cómo usar?
- Desigualdades:
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4+12x>7+13x
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x-4x^2/x-1>0
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x^2-17x+72>0
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(x-9)*(x-1)>0
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Expresiones idénticas
- tres tg^2x-4sqrt3tgx+3< cero
- 3tg al cuadrado x menos 4 raíz cuadrada de 3tgx más 3 menos 0
- tres tg al cuadrado x menos 4 raíz cuadrada de 3tgx más 3 menos cero
- 3tg^2x-4√3tgx+3<0
- 3tg2x-4sqrt3tgx+3<0
- 3tg²x-4sqrt3tgx+3<0
- 3tg en el grado 2x-4sqrt3tgx+3<0
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Expresiones semejantes
- 3tg^2x+4sqrt3tgx+3<0
- 3tg^2x-4sqrt3tgx-3<0
3tg^2x-4sqrt3tgx+3<0 desigualdades
Solución
Ha introducido
[src]
2 __________ 3*tan (x) - 4*\/ 3*tan(x) + 3 < 0
$$\left(- 4 \sqrt{3 \tan{\left(x \right)}} + 3 \tan^{2}{\left(x \right)}\right) + 3 < 0$$
-4*sqrt(3)*sqrt(tan(x)) + 3*tan(x)^2 + 3 < 0
Solución detallada
Se da la desigualdad:
$$\left(- 4 \sqrt{3 \tan{\left(x \right)}} + 3 \tan^{2}{\left(x \right)}\right) + 3 < 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(- 4 \sqrt{3 \tan{\left(x \right)}} + 3 \tan^{2}{\left(x \right)}\right) + 3 = 0$$
Resolvemos:
$$x_{1} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$x_{2} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(\sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$x_{1} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$x_{2} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(\sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
Las raíces dadas
$$x_{1} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$x_{2} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(\sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{1}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
=
$$- \frac{1}{10} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
lo sustituimos en la expresión
$$\left(- 4 \sqrt{3 \tan{\left(x \right)}} + 3 \tan^{2}{\left(x \right)}\right) + 3 < 0$$
$$\left(- 4 \sqrt{3 \tan{\left(- \frac{1}{10} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)} \right)}} + 3 \tan^{2}{\left(- \frac{1}{10} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)} \right)}\right) + 3 < 0$$
pero
Entonces
$$x < \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)} \wedge x < \operatorname{atan}{\left(\frac{\sqrt{3} \left(\sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$\left(- 4 \sqrt{3 \tan{\left(x \right)}} + 3 \tan^{2}{\left(x \right)}\right) + 3 < 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(- 4 \sqrt{3 \tan{\left(x \right)}} + 3 \tan^{2}{\left(x \right)}\right) + 3 = 0$$
Resolvemos:
$$x_{1} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$x_{2} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(\sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$x_{1} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$x_{2} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(\sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
Las raíces dadas
$$x_{1} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
$$x_{2} = \operatorname{atan}{\left(\frac{\sqrt{3} \left(\sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{1}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
=
$$- \frac{1}{10} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
lo sustituimos en la expresión
$$\left(- 4 \sqrt{3 \tan{\left(x \right)}} + 3 \tan^{2}{\left(x \right)}\right) + 3 < 0$$
$$\left(- 4 \sqrt{3 \tan{\left(- \frac{1}{10} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)} \right)}} + 3 \tan^{2}{\left(- \frac{1}{10} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)} \right)}\right) + 3 < 0$$
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| | | 3/4 / ______________________________________________ ______________________________________________ ||| / | | | 3/4 / ______________________________________________ ______________________________________________ |||
| | |/ _____________ / _____________\\ / / _____________ / _____________\ _____________ / _____________ / _____________\ _____________ / _____________\ ||| / | | |/ _____________ / _____________\\ / / _____________ / _____________\ _____________ / _____________ / _____________\ _____________ / _____________\ |||
| | ___ || 3 / ___ | 3 / ___ || / / 3 / ___ | 3 / ___ | ___ / ___ / 3 / ___ | 3 / ___ | 3 / ___ | 3 / ___ | ||| / | | ___ || 3 / ___ | 3 / ___ || / / 3 / ___ | 3 / ___ | ___ / ___ / 3 / ___ | 3 / ___ | 3 / ___ | 3 / ___ | |||
2|1 |\/ 3 *\\1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 // - \/ - \/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / + 4*\/ 3 *\/ 5 + 2*\/ 6 - \/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / *\/ 5 + 2*\/ 6 *\2 + \/ 5 + 2*\/ 6 / /|| ___ / |1 |\/ 3 *\\1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 // - \/ - \/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / + 4*\/ 3 *\/ 5 + 2*\/ 6 - \/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / *\/ 5 + 2*\/ 6 *\2 + \/ 5 + 2*\/ 6 / /|| < 0
3 + 3*tan |-- - atan|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| - 4*\/ 3 * / -tan|-- - atan|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
|10 | ______________________________________________ || / |10 | ______________________________________________ ||
| | / _____________ / _____________\ _____________ || / | | / _____________ / _____________\ _____________ ||
| | 4 / 3 / ___ | 3 / ___ | 6 / ___ || / | | 4 / 3 / ___ | 3 / ___ | 6 / ___ ||
\ \ 3*\/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / *\/ 5 + 2*\/ 6 // \/ \ \ 3*\/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / *\/ 5 + 2*\/ 6 // pero
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/ / / ______________________________________________________________________________________________________________________________________________________________________________\\\ / / / / ______________________________________________________________________________________________________________________________________________________________________________\\\
| | | 3/4 / ______________________________________________ ______________________________________________ ||| / | | | 3/4 / ______________________________________________ ______________________________________________ |||
| | |/ _____________ / _____________\\ / / _____________ / _____________\ _____________ / _____________ / _____________\ _____________ / _____________\ ||| / | | |/ _____________ / _____________\\ / / _____________ / _____________\ _____________ / _____________ / _____________\ _____________ / _____________\ |||
| | ___ || 3 / ___ | 3 / ___ || / / 3 / ___ | 3 / ___ | ___ / ___ / 3 / ___ | 3 / ___ | 3 / ___ | 3 / ___ | ||| / | | ___ || 3 / ___ | 3 / ___ || / / 3 / ___ | 3 / ___ | ___ / ___ / 3 / ___ | 3 / ___ | 3 / ___ | 3 / ___ | |||
2|1 |\/ 3 *\\1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 // - \/ - \/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / + 4*\/ 3 *\/ 5 + 2*\/ 6 - \/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / *\/ 5 + 2*\/ 6 *\2 + \/ 5 + 2*\/ 6 / /|| ___ / |1 |\/ 3 *\\1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 // - \/ - \/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / + 4*\/ 3 *\/ 5 + 2*\/ 6 - \/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / *\/ 5 + 2*\/ 6 *\2 + \/ 5 + 2*\/ 6 / /|| > 0
3 + 3*tan |-- - atan|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| - 4*\/ 3 * / -tan|-- - atan|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
|10 | ______________________________________________ || / |10 | ______________________________________________ ||
| | / _____________ / _____________\ _____________ || / | | / _____________ / _____________\ _____________ ||
| | 4 / 3 / ___ | 3 / ___ | 6 / ___ || / | | 4 / 3 / ___ | 3 / ___ | 6 / ___ ||
\ \ 3*\/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / *\/ 5 + 2*\/ 6 // \/ \ \ 3*\/ 1 + \/ 5 + 2*\/ 6 *\-1 + \/ 5 + 2*\/ 6 / *\/ 5 + 2*\/ 6 // Entonces
$$x < \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)} \wedge x < \operatorname{atan}{\left(\frac{\sqrt{3} \left(\sqrt{- \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \left(2 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5} - \sqrt{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} + 4 \sqrt{3} \sqrt{2 \sqrt{6} + 5}} + \left(1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{1 + \left(-1 + \sqrt[3]{2 \sqrt{6} + 5}\right) \sqrt[3]{2 \sqrt{6} + 5}} \sqrt[6]{2 \sqrt{6} + 5}} \right)}$$
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x1 x2
Solución de la desigualdad en el gráfico