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- La ecuación:
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Ecuación x+4=0
-
Ecuación x*(x^2+8*x+16)=5*(x+4)
- Ecuación z^2+3+4*i=0
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Ecuación x^2+3x+2=0
- Expresar {x} en función de y en la ecuación:
- 18*x-11*y=2
- 5*x+4*y=-12
- 12*x-14*y=20
- -3*x-20*y=-13
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Expresiones idénticas
- x^ dos - dos *sqrt(tres *x)- uno = cero
- x al cuadrado menos 2 multiplicar por raíz cuadrada de (3 multiplicar por x) menos 1 es igual a 0
- x en el grado dos menos dos multiplicar por raíz cuadrada de (tres multiplicar por x) menos uno es igual a cero
- x^2-2*√(3*x)-1=0
- x2-2*sqrt(3*x)-1=0
- x2-2*sqrt3*x-1=0
- x²-2*sqrt(3*x)-1=0
- x en el grado 2-2*sqrt(3*x)-1=0
- x^2-2sqrt(3x)-1=0
- x2-2sqrt(3x)-1=0
- x2-2sqrt3x-1=0
- x^2-2sqrt3x-1=0
- x^2-2*sqrt(3*x)-1=O
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Expresiones semejantes
- x^2-2*sqrt(3*x)+1=0
- x^2+2*sqrt(3*x)-1=0
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x+4)=x-3
- sqrt(6+5*x)=x
- sqrt(x-2)=6
- sqrt(2*x+3)=x
- sqrt(x^2-5x+1)=sqrt(x-4)
x^2-2*sqrt(3*x)-1=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Suma y producto de raíces
[src]
suma
_______________________________________________________________________________________________________________________
/ _______________
/ / _____
/ 8 / 251 \/ 777 24 8
/ - - 2*3 / --- + ------- + --------------------------------------------------------------- - ----------------------
_____________________________________________________ / 3 \/ 27 3 _____________________________________________________ _______________
/ _______________ / / _______________ / _____
/ / _____ / / / _____ / 251 \/ 777
/ 4 / 251 \/ 777 8 / / 4 / 251 \/ 777 8 9*3 / --- + -------
/ - + 2*3 / --- + ------- + ---------------------- / / - + 2*3 / --- + ------- + ---------------------- \/ 27 3
/ 3 \/ 27 3 _______________ / / 3 \/ 27 3 _______________
/ / _____ / / / _____
/ / 251 \/ 777 / / / 251 \/ 777
/ 9*3 / --- + ------- / / 9*3 / --- + -------
\/ \/ 27 3 \/ \/ \/ 27 3
--------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}} - \frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{8}{3} + \frac{24}{\sqrt{\frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}}}}}{2} + \frac{\sqrt{\frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}}}{2}$$
=
_______________________________________________________________________________________________________________________
/ _______________
/ / _____
/ 8 / 251 \/ 777 24 8
/ - - 2*3 / --- + ------- + --------------------------------------------------------------- - ----------------------
_____________________________________________________ / 3 \/ 27 3 _____________________________________________________ _______________
/ _______________ / / _______________ / _____
/ / _____ / / / _____ / 251 \/ 777
/ 4 / 251 \/ 777 8 / / 4 / 251 \/ 777 8 9*3 / --- + -------
/ - + 2*3 / --- + ------- + ---------------------- / / - + 2*3 / --- + ------- + ---------------------- \/ 27 3
/ 3 \/ 27 3 _______________ / / 3 \/ 27 3 _______________
/ / _____ / / / _____
/ / 251 \/ 777 / / / 251 \/ 777
/ 9*3 / --- + ------- / / 9*3 / --- + -------
\/ \/ 27 3 \/ \/ \/ 27 3
--------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}} - \frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{8}{3} + \frac{24}{\sqrt{\frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}}}}}{2} + \frac{\sqrt{\frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}}}{2}$$
producto
_______________________________________________________________________________________________________________________
/ _______________
/ / _____
/ 8 / 251 \/ 777 24 8
/ - - 2*3 / --- + ------- + --------------------------------------------------------------- - ----------------------
_____________________________________________________ / 3 \/ 27 3 _____________________________________________________ _______________
/ _______________ / / _______________ / _____
/ / _____ / / / _____ / 251 \/ 777
/ 4 / 251 \/ 777 8 / / 4 / 251 \/ 777 8 9*3 / --- + -------
/ - + 2*3 / --- + ------- + ---------------------- / / - + 2*3 / --- + ------- + ---------------------- \/ 27 3
/ 3 \/ 27 3 _______________ / / 3 \/ 27 3 _______________
/ / _____ / / / _____
/ / 251 \/ 777 / / / 251 \/ 777
/ 9*3 / --- + ------- / / 9*3 / --- + -------
\/ \/ 27 3 \/ \/ \/ 27 3
--------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}} - \frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{8}{3} + \frac{24}{\sqrt{\frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}}}}}{2} + \frac{\sqrt{\frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}}}{2}$$
=
/ ___________________________________________________________________________________________________________________________________________________________________________________________________________\
| 3/4 / _____________________________________________________ _____________________________________________________ |
|/ _________________ / _________________\\ / / _________________ / _________________\ _________________ / _________________ / _________________\ _________________ / _________________\ |
___ || 3 / _____ | 3 / _____ || / / 3 / _____ | 3 / _____ | ___ / _____ / 3 / _____ | 3 / _____ | 3 / _____ | 3 / _____ | |
\/ 6 *\\4 + \/ 251 + 9*\/ 777 *\2 + \/ 251 + 9*\/ 777 // + \/ - 4*\/ 4 + \/ 251 + 9*\/ 777 *\2 + \/ 251 + 9*\/ 777 / + 18*\/ 6 *\/ 251 + 9*\/ 777 + \/ 4 + \/ 251 + 9*\/ 777 *\2 + \/ 251 + 9*\/ 777 / *\/ 251 + 9*\/ 777 *\4 - \/ 251 + 9*\/ 777 / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_____________________________________________________
/ _________________ / _________________\ _________________
4 / 3 / _____ | 3 / _____ | 6 / _____
6*\/ 4 + \/ 251 + 9*\/ 777 *\2 + \/ 251 + 9*\/ 777 / *\/ 251 + 9*\/ 777
$$\frac{\sqrt{6} \left(\sqrt{\sqrt{4 + \left(2 + \sqrt[3]{9 \sqrt{777} + 251}\right) \sqrt[3]{9 \sqrt{777} + 251}} \left(4 - \sqrt[3]{9 \sqrt{777} + 251}\right) \sqrt[3]{9 \sqrt{777} + 251} - 4 \sqrt{4 + \left(2 + \sqrt[3]{9 \sqrt{777} + 251}\right) \sqrt[3]{9 \sqrt{777} + 251}} + 18 \sqrt{6} \sqrt{9 \sqrt{777} + 251}} + \left(4 + \left(2 + \sqrt[3]{9 \sqrt{777} + 251}\right) \sqrt[3]{9 \sqrt{777} + 251}\right)^{\frac{3}{4}}\right)}{6 \sqrt[4]{4 + \left(2 + \sqrt[3]{9 \sqrt{777} + 251}\right) \sqrt[3]{9 \sqrt{777} + 251}} \sqrt[6]{9 \sqrt{777} + 251}}$$
sqrt(6)*((4 + (251 + 9*sqrt(777))^(1/3)*(2 + (251 + 9*sqrt(777))^(1/3)))^(3/4) + sqrt(-4*sqrt(4 + (251 + 9*sqrt(777))^(1/3)*(2 + (251 + 9*sqrt(777))^(1/3))) + 18*sqrt(6)*sqrt(251 + 9*sqrt(777)) + sqrt(4 + (251 + 9*sqrt(777))^(1/3)*(2 + (251 + 9*sqrt(777))^(1/3)))*(251 + 9*sqrt(777))^(1/3)*(4 - (251 + 9*sqrt(777))^(1/3))))/(6*(4 + (251 + 9*sqrt(777))^(1/3)*(2 + (251 + 9*sqrt(777))^(1/3)))^(1/4)*(251 + 9*sqrt(777))^(1/6))
Respuesta rápida
[src]
_______________________________________________________________________________________________________________________
/ _______________
/ / _____
/ 8 / 251 \/ 777 24 8
/ - - 2*3 / --- + ------- + --------------------------------------------------------------- - ----------------------
_____________________________________________________ / 3 \/ 27 3 _____________________________________________________ _______________
/ _______________ / / _______________ / _____
/ / _____ / / / _____ / 251 \/ 777
/ 4 / 251 \/ 777 8 / / 4 / 251 \/ 777 8 9*3 / --- + -------
/ - + 2*3 / --- + ------- + ---------------------- / / - + 2*3 / --- + ------- + ---------------------- \/ 27 3
/ 3 \/ 27 3 _______________ / / 3 \/ 27 3 _______________
/ / _____ / / / _____
/ / 251 \/ 777 / / / 251 \/ 777
/ 9*3 / --- + ------- / / 9*3 / --- + -------
\/ \/ 27 3 \/ \/ \/ 27 3
x1 = --------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{1} = \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}} - \frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{8}{3} + \frac{24}{\sqrt{\frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}}}}}{2} + \frac{\sqrt{\frac{8}{9 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{\sqrt{777}}{3} + \frac{251}{27}}}}{2}$$
x1 = sqrt(-2*(sqrt(777)/3 + 251/27)^(1/3) - 8/(9*(sqrt(777)/3 + 251/27)^(1/3)) + 8/3 + 24/sqrt(8/(9*(sqrt(777)/3 + 251/27)^(1/3)) + 4/3 + 2*(sqrt(777)/3 + 251/27)^(1/3)))/2 + sqrt(8/(9*(sqrt(777)/3 + 251/27)^(1/3)) + 4/3 + 2*(sqrt(777)/3 + 251/27)^(1/3))/2