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Otras calculadoras
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- La ecuación:
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Ecuación 2*x^2+6*x+9=0
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Ecuación cos(x)=2
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Ecuación sqrt(x^2-x-1)-sqrt(x)=1
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Ecuación sin(x/4)=1/2
- Expresar {x} en función de y en la ecuación:
- 10*x+5*y=-17
- 16*x-17*y=-9
- -10*x+16*y=-6
- 2*x+2*y=-6
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Expresiones idénticas
- sqrt(x^ dos -x- uno)-sqrt(x)= uno
- raíz cuadrada de (x al cuadrado menos x menos 1) menos raíz cuadrada de (x) es igual a 1
- raíz cuadrada de (x en el grado dos menos x menos uno) menos raíz cuadrada de (x) es igual a uno
- √(x^2-x-1)-√(x)=1
- sqrt(x2-x-1)-sqrt(x)=1
- sqrtx2-x-1-sqrtx=1
- sqrt(x²-x-1)-sqrt(x)=1
- sqrt(x en el grado 2-x-1)-sqrt(x)=1
- sqrtx^2-x-1-sqrtx=1
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Expresiones semejantes
- sqrt(x^2-x+1)-sqrt(x)=1
- sqrt(x^2-x-1)+sqrt(x)=1
- sqrt(x^2+x-1)-sqrt(x)=1
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x)=-1
- sqrt(x)+1=x-1
- sqrt(3-x)=1-x
- sqrt(x-1)=3
- sqrt(x^2-16)=8-x
- Raíz cuadrada sqrt
- sqrt(x)=-1
- sqrt(x)+1=x-1
- sqrt(3-x)=1-x
- sqrt(x-1)=3
- sqrt(x^2-16)=8-x
sqrt(x^2-x-1)-sqrt(x)=1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
____________ / 2 ___ \/ x - x - 1 - \/ x = 1
$$- \sqrt{x} + \sqrt{\left(x^{2} - x\right) - 1} = 1$$
Respuesta rápida
[src]
_______________________________________________________________________________________________________________
/ _____________
/ / _____
/ / \/ 489 8 16
/ 8 - 2*3 / 5 + ------- + ----------------------------------------------------------- - --------------------
_________________________________________________ / \/ 9 _________________________________________________ _____________
/ _____________ / / _____________ / _____
/ / _____ / / / _____ / \/ 489
/ / \/ 489 16 / / / \/ 489 16 3*3 / 5 + -------
/ 4 + 2*3 / 5 + ------- + -------------------- / / 4 + 2*3 / 5 + ------- + -------------------- \/ 9
/ \/ 9 _____________ / / \/ 9 _____________
/ / _____ / / / _____
/ / \/ 489 / / / \/ 489
/ 3*3 / 5 + ------- / / 3*3 / 5 + -------
\/ \/ 9 \/ \/ \/ 9
x1 = 1 + ----------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{1} = \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} - \frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}} + 8}}{2} + 1 + \frac{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}}{2}$$
x1 = sqrt(-2*(sqrt(489)/9 + 5)^(1/3) - 16/(3*(sqrt(489)/9 + 5)^(1/3)) + 8/sqrt(16/(3*(sqrt(489)/9 + 5)^(1/3)) + 2*(sqrt(489)/9 + 5)^(1/3) + 4) + 8)/2 + 1 + sqrt(16/(3*(sqrt(489)/9 + 5)^(1/3)) + 2*(sqrt(489)/9 + 5)^(1/3) + 4)/2
Suma y producto de raíces
[src]
suma
_______________________________________________________________________________________________________________
/ _____________
/ / _____
/ / \/ 489 8 16
/ 8 - 2*3 / 5 + ------- + ----------------------------------------------------------- - --------------------
_________________________________________________ / \/ 9 _________________________________________________ _____________
/ _____________ / / _____________ / _____
/ / _____ / / / _____ / \/ 489
/ / \/ 489 16 / / / \/ 489 16 3*3 / 5 + -------
/ 4 + 2*3 / 5 + ------- + -------------------- / / 4 + 2*3 / 5 + ------- + -------------------- \/ 9
/ \/ 9 _____________ / / \/ 9 _____________
/ / _____ / / / _____
/ / \/ 489 / / / \/ 489
/ 3*3 / 5 + ------- / / 3*3 / 5 + -------
\/ \/ 9 \/ \/ \/ 9
1 + ----------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} - \frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}} + 8}}{2} + 1 + \frac{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}}{2}$$
=
_______________________________________________________________________________________________________________
/ _____________
/ / _____
/ / \/ 489 8 16
/ 8 - 2*3 / 5 + ------- + ----------------------------------------------------------- - --------------------
_________________________________________________ / \/ 9 _________________________________________________ _____________
/ _____________ / / _____________ / _____
/ / _____ / / / _____ / \/ 489
/ / \/ 489 16 / / / \/ 489 16 3*3 / 5 + -------
/ 4 + 2*3 / 5 + ------- + -------------------- / / 4 + 2*3 / 5 + ------- + -------------------- \/ 9
/ \/ 9 _____________ / / \/ 9 _____________
/ / _____ / / / _____
/ / \/ 489 / / / \/ 489
/ 3*3 / 5 + ------- / / 3*3 / 5 + -------
\/ \/ 9 \/ \/ \/ 9
1 + ----------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} - \frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}} + 8}}{2} + 1 + \frac{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}}{2}$$
producto
_______________________________________________________________________________________________________________
/ _____________
/ / _____
/ / \/ 489 8 16
/ 8 - 2*3 / 5 + ------- + ----------------------------------------------------------- - --------------------
_________________________________________________ / \/ 9 _________________________________________________ _____________
/ _____________ / / _____________ / _____
/ / _____ / / / _____ / \/ 489
/ / \/ 489 16 / / / \/ 489 16 3*3 / 5 + -------
/ 4 + 2*3 / 5 + ------- + -------------------- / / 4 + 2*3 / 5 + ------- + -------------------- \/ 9
/ \/ 9 _____________ / / \/ 9 _____________
/ / _____ / / / _____
/ / \/ 489 / / / \/ 489
/ 3*3 / 5 + ------- / / 3*3 / 5 + -------
\/ \/ 9 \/ \/ \/ 9
1 + ----------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} - \frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}} + 8}}{2} + 1 + \frac{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}}{2}$$
=
_______________________________________________________________________________________________________________
/ _____________
/ / _____
/ / \/ 489 8 16
/ 8 - 2*3 / 5 + ------- + ----------------------------------------------------------- - --------------------
_________________________________________________ / \/ 9 _________________________________________________ _____________
/ _____________ / / _____________ / _____
/ / _____ / / / _____ / \/ 489
/ / \/ 489 16 / / / \/ 489 16 3*3 / 5 + -------
/ 4 + 2*3 / 5 + ------- + -------------------- / / 4 + 2*3 / 5 + ------- + -------------------- \/ 9
/ \/ 9 _____________ / / \/ 9 _____________
/ / _____ / / / _____
/ / \/ 489 / / / \/ 489
/ 3*3 / 5 + ------- / / 3*3 / 5 + -------
\/ \/ 9 \/ \/ \/ 9
1 + ----------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} - \frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}} + 8}}{2} + 1 + \frac{\sqrt{\frac{16}{3 \sqrt[3]{\frac{\sqrt{489}}{9} + 5}} + 2 \sqrt[3]{\frac{\sqrt{489}}{9} + 5} + 4}}{2}$$
1 + sqrt(4 + 2*(5 + sqrt(489)/9)^(1/3) + 16/(3*(5 + sqrt(489)/9)^(1/3)))/2 + sqrt(8 - 2*(5 + sqrt(489)/9)^(1/3) + 8/sqrt(4 + 2*(5 + sqrt(489)/9)^(1/3) + 16/(3*(5 + sqrt(489)/9)^(1/3))) - 16/(3*(5 + sqrt(489)/9)^(1/3)))/2
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