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- La ecuación:
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Ecuación x^2+5x=36
-
Ecuación 3*x-6=x+4
-
Ecuación 9^x-8*3^x-9=0
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Ecuación x^3+4=0
- Expresar {x} en función de y en la ecuación:
- -2*x-19*y=3
- 6*x+17*y=-11
- -11*x-7*y=-2
- -19*x+14*y=20
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Expresiones idénticas
- x^ tres +2 cero 22x+sqrt(dos mil veintiuno)=0
- x al cubo más 2022x más raíz cuadrada de (2021) es igual a 0
- x en el grado tres más 2 cero 22x más raíz cuadrada de (dos mil veintiuno) es igual a 0
- x^3+2022x+√(2021)=0
- x3+2022x+sqrt(2021)=0
- x3+2022x+sqrt2021=0
- x³+2022x+sqrt(2021)=0
- x en el grado 3+2022x+sqrt(2021)=0
- x^3+2022x+sqrt2021=0
- x^3+2022x+sqrt(2021)=O
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Expresiones semejantes
- x^3+2022x-sqrt(2021)=0
- x^3-2022x+sqrt(2021)=0
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x+2)-sqrt(x-6)=2
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(5+2*x)=8+-sqrt(x-1)
- sqrt(4*x^2+4*x-6)=2
x^3+2022x+sqrt(2021)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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3 ______ x + 2022*x + \/ 2021 = 0
$$\left(x^{3} + 2022 x\right) + \sqrt{2021} = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2022$$
$$v = \frac{d}{a}$$
$$v = \sqrt{2021}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2022$$
$$x_{1} x_{2} x_{3} = \sqrt{2021}$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2022$$
$$v = \frac{d}{a}$$
$$v = \sqrt{2021}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2022$$
$$x_{1} x_{2} x_{3} = \sqrt{2021}$$
Suma y producto de raíces
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suma
_________________________________ / _________________________________\ _________________________________ / _________________________________\ _________________________________
/ ______ ____________ | / ______ ____________ | / ______ ____________ | / ______ ____________ | / ______ ____________
/ 27*\/ 2021 27*\/ 1224730117 | ___ / 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117 | ___ / 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117
3 / ----------- + ----------------- | ___ \/ 3 *3 / ----------- + ----------------- | 3 / ----------- + ----------------- | ___ \/ 3 *3 / ----------- + ----------------- | 3 / ----------- + -----------------
1011 \/ 2 2 | 1011*\/ 3 \/ 2 2 | 1011 \/ 2 2 | 1011*\/ 3 \/ 2 2 | 2022 \/ 2 2
- -------------------------------------- + -------------------------------------- + I*|-------------------------------------- + --------------------------------------------| + - -------------------------------------- + -------------------------------------- + I*|- -------------------------------------- - --------------------------------------------| + -------------------------------------- - --------------------------------------
_________________________________ 6 | _________________________________ 6 | _________________________________ 6 | _________________________________ 6 | _________________________________ 3
/ ______ ____________ | / ______ ____________ | / ______ ____________ | / ______ ____________ | / ______ ____________
/ 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117
3 / ----------- + ----------------- |3 / ----------- + ----------------- | 3 / ----------- + ----------------- | 3 / ----------- + ----------------- | 3 / ----------- + -----------------
\/ 2 2 \\/ 2 2 / \/ 2 2 \ \/ 2 2 / \/ 2 2
$$\left(- \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{3} + \frac{2022}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right) + \left(\left(- \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} - \frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right)\right) + \left(- \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(\frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6}\right)\right)\right)$$
=
/ _________________________________\ / _________________________________\ | / ______ ____________ | | / ______ ____________ | | ___ / 27*\/ 2021 27*\/ 1224730117 | | ___ / 27*\/ 2021 27*\/ 1224730117 | | ___ \/ 3 *3 / ----------- + ----------------- | | ___ \/ 3 *3 / ----------- + ----------------- | | 1011*\/ 3 \/ 2 2 | | 1011*\/ 3 \/ 2 2 | I*|- -------------------------------------- - --------------------------------------------| + I*|-------------------------------------- + --------------------------------------------| | _________________________________ 6 | | _________________________________ 6 | | / ______ ____________ | | / ______ ____________ | | / 27*\/ 2021 27*\/ 1224730117 | | / 27*\/ 2021 27*\/ 1224730117 | | 3 / ----------- + ----------------- | |3 / ----------- + ----------------- | \ \/ 2 2 / \\/ 2 2 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} - \frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right) + i \left(\frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6}\right)$$
producto
/ _________________________________ / _________________________________\\ / _________________________________ / _________________________________\\ / _________________________________\ | / ______ ____________ | / ______ ____________ || | / ______ ____________ | / ______ ____________ || | / ______ ____________ | | / 27*\/ 2021 27*\/ 1224730117 | ___ / 27*\/ 2021 27*\/ 1224730117 || | / 27*\/ 2021 27*\/ 1224730117 | ___ / 27*\/ 2021 27*\/ 1224730117 || | / 27*\/ 2021 27*\/ 1224730117 | | 3 / ----------- + ----------------- | ___ \/ 3 *3 / ----------- + ----------------- || | 3 / ----------- + ----------------- | ___ \/ 3 *3 / ----------- + ----------------- || | 3 / ----------- + ----------------- | | 1011 \/ 2 2 | 1011*\/ 3 \/ 2 2 || | 1011 \/ 2 2 | 1011*\/ 3 \/ 2 2 || | 2022 \/ 2 2 | |- -------------------------------------- + -------------------------------------- + I*|-------------------------------------- + --------------------------------------------||*|- -------------------------------------- + -------------------------------------- + I*|- -------------------------------------- - --------------------------------------------||*|-------------------------------------- - --------------------------------------| | _________________________________ 6 | _________________________________ 6 || | _________________________________ 6 | _________________________________ 6 || | _________________________________ 3 | | / ______ ____________ | / ______ ____________ || | / ______ ____________ | / ______ ____________ || | / ______ ____________ | | / 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117 || | / 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117 || | / 27*\/ 2021 27*\/ 1224730117 | | 3 / ----------- + ----------------- |3 / ----------- + ----------------- || | 3 / ----------- + ----------------- | 3 / ----------- + ----------------- || |3 / ----------- + ----------------- | \ \/ 2 2 \\/ 2 2 // \ \/ 2 2 \ \/ 2 2 // \\/ 2 2 /
$$\left(- \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(\frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6}\right)\right) \left(- \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} - \frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{3} + \frac{2022}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right)$$
=
/ _______________\ -\2021 + \/ 2475179566457 / ---------------------------- ______ ____________ \/ 2021 + \/ 1224730117
$$- \frac{2021 + \sqrt{2475179566457}}{\sqrt{2021} + \sqrt{1224730117}}$$
-(2021 + sqrt(2475179566457))/(sqrt(2021) + sqrt(1224730117))
Respuesta rápida
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_________________________________ / _________________________________\
/ ______ ____________ | / ______ ____________ |
/ 27*\/ 2021 27*\/ 1224730117 | ___ / 27*\/ 2021 27*\/ 1224730117 |
3 / ----------- + ----------------- | ___ \/ 3 *3 / ----------- + ----------------- |
1011 \/ 2 2 | 1011*\/ 3 \/ 2 2 |
x1 = - -------------------------------------- + -------------------------------------- + I*|-------------------------------------- + --------------------------------------------|
_________________________________ 6 | _________________________________ 6 |
/ ______ ____________ | / ______ ____________ |
/ 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117 |
3 / ----------- + ----------------- |3 / ----------- + ----------------- |
\/ 2 2 \\/ 2 2 /
$$x_{1} = - \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(\frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6}\right)$$
_________________________________ / _________________________________\
/ ______ ____________ | / ______ ____________ |
/ 27*\/ 2021 27*\/ 1224730117 | ___ / 27*\/ 2021 27*\/ 1224730117 |
3 / ----------- + ----------------- | ___ \/ 3 *3 / ----------- + ----------------- |
1011 \/ 2 2 | 1011*\/ 3 \/ 2 2 |
x2 = - -------------------------------------- + -------------------------------------- + I*|- -------------------------------------- - --------------------------------------------|
_________________________________ 6 | _________________________________ 6 |
/ ______ ____________ | / ______ ____________ |
/ 27*\/ 2021 27*\/ 1224730117 | / 27*\/ 2021 27*\/ 1224730117 |
3 / ----------- + ----------------- | 3 / ----------- + ----------------- |
\/ 2 2 \ \/ 2 2 /
$$x_{2} = - \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} - \frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right)$$
_________________________________
/ ______ ____________
/ 27*\/ 2021 27*\/ 1224730117
3 / ----------- + -----------------
2022 \/ 2 2
x3 = -------------------------------------- - --------------------------------------
_________________________________ 3
/ ______ ____________
/ 27*\/ 2021 27*\/ 1224730117
3 / ----------- + -----------------
\/ 2 2
$$x_{3} = - \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{3} + \frac{2022}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}$$
x3 = -(27*sqrt(2021)/2 + 27*sqrt(1224730117)/2)^(1/3)/3 + 2022/(27*sqrt(2021)/2 + 27*sqrt(1224730117)/2)^(1/3)
Respuesta numérica
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x1 = 0.011116598070172 + 44.9666584341805*i
x2 = -0.0222331961403439
x3 = 0.011116598070172 - 44.9666584341805*i
x3 = 0.011116598070172 - 44.9666584341805*i