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- La ecuación:
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Ecuación x-3√x+2=0
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Ecuación -33-y=19
- Ecuación x2-x-1=0
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Ecuación x^2+4*x-5=0
- Expresar {x} en función de y en la ecuación:
- -8*x-6*y=-20
- -20*x+1*y=12
- -6*x-8*y=18
- -11*x-18*y=18
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Expresiones idénticas
- uno +(x^ tres -x^ dos -x- uno)/(x^ cuatro - dos *x^ dos)= cero
- 1 más (x al cubo menos x al cuadrado menos x menos 1) dividir por (x en el grado 4 menos 2 multiplicar por x al cuadrado ) es igual a 0
- uno más (x en el grado tres menos x en el grado dos menos x menos uno) dividir por (x en el grado cuatro menos dos multiplicar por x en el grado dos) es igual a cero
- 1+(x3-x2-x-1)/(x4-2*x2)=0
- 1+x3-x2-x-1/x4-2*x2=0
- 1+(x³-x²-x-1)/(x⁴-2*x²)=0
- 1+(x en el grado 3-x en el grado 2-x-1)/(x en el grado 4-2*x en el grado 2)=0
- 1+(x^3-x^2-x-1)/(x^4-2x^2)=0
- 1+(x3-x2-x-1)/(x4-2x2)=0
- 1+x3-x2-x-1/x4-2x2=0
- 1+x^3-x^2-x-1/x^4-2x^2=0
- 1+(x^3-x^2-x-1)/(x^4-2*x^2)=O
- 1+(x^3-x^2-x-1) dividir por (x^4-2*x^2)=0
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Expresiones semejantes
- 1-(x^3-x^2-x-1)/(x^4-2*x^2)=0
- 1+(x^3-x^2-x-1)/(x^4+2*x^2)=0
- 1+(x^3-x^2+x-1)/(x^4-2*x^2)=0
- 1+(x^3+x^2-x-1)/(x^4-2*x^2)=0
- 1+(x^3-x^2-x+1)/(x^4-2*x^2)=0
1+(x^3-x^2-x-1)/(x^4-2*x^2)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2
x - x - x - 1
1 + --------------- = 0
4 2
x - 2*x
$$1 + \frac{\left(- x + \left(x^{3} - x^{2}\right)\right) - 1}{x^{4} - 2 x^{2}} = 0$$
Suma y producto de raíces
[src]
suma
_________________________________ ___________________________________ ___________________________________ _________________________________
/ 9 3 ____ 5 / |9 3 ____ 5 | / |9 3 ____ 5 | / 9 3 ____ 5
/ - + \/ 11 + ------------------ I* / |- + \/ 11 - ------------------| I* / |- + \/ 11 - ------------------| / - + \/ 11 + ------------------
/ 2 ____________ ____________ ____________ / |2 ____________| ____________ / |2 ____________| ____________ / 2 ____________
/ / 9 3 ____ / 9 3 ____ / 9 3 ____ / | / 9 3 ____ | / 9 3 ____ / | / 9 3 ____ | / 9 3 ____ / / 9 3 ____
/ 4* / - - \/ 11 / - - \/ 11 / - - \/ 11 / | 4* / - - \/ 11 | / - - \/ 11 / | 4* / - - \/ 11 | / - - \/ 11 / 4* / - - \/ 11
1 \/ \/ 4 \/ 4 1 \/ 4 \/ | \/ 4 | 1 \/ 4 \/ | \/ 4 | 1 \/ 4 \/ \/ 4
- - + ---------------------------------------- - ---------------- + - - + ---------------- - -------------------------------------------- + - - + ---------------- + -------------------------------------------- + - - - ---------------- - ----------------------------------------
4 2 2 4 2 2 4 2 2 4 2 2
$$\left(- \frac{\sqrt{\sqrt[3]{11} + \frac{9}{2} + \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}}}}{2} - \frac{1}{4} - \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2}\right) + \left(\left(\left(- \frac{1}{4} - \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} + \frac{\sqrt{\sqrt[3]{11} + \frac{9}{2} + \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}}}}{2}\right) + \left(- \frac{1}{4} + \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} - \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}} + \sqrt[3]{11} + \frac{9}{2}}\right|}}{2}\right)\right) + \left(- \frac{1}{4} + \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} + \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}} + \sqrt[3]{11} + \frac{9}{2}}\right|}}{2}\right)\right)$$
=
-1
$$-1$$
producto
/ _________________________________ \ / ___________________________________\ / ___________________________________\ / _________________________________\ | / 9 3 ____ 5 | | / |9 3 ____ 5 | | | / |9 3 ____ 5 | | | / 9 3 ____ 5 | | / - + \/ 11 + ------------------ | | I* / |- + \/ 11 - ------------------| | | I* / |- + \/ 11 - ------------------| | | / - + \/ 11 + ------------------ | | / 2 ____________ ____________| | ____________ / |2 ____________| | | ____________ / |2 ____________| | | ____________ / 2 ____________ | | / / 9 3 ____ / 9 3 ____ | | / 9 3 ____ / | / 9 3 ____ | | | / 9 3 ____ / | / 9 3 ____ | | | / 9 3 ____ / / 9 3 ____ | | / 4* / - - \/ 11 / - - \/ 11 | | / - - \/ 11 / | 4* / - - \/ 11 | | | / - - \/ 11 / | 4* / - - \/ 11 | | | / - - \/ 11 / 4* / - - \/ 11 | | 1 \/ \/ 4 \/ 4 | | 1 \/ 4 \/ | \/ 4 | | | 1 \/ 4 \/ | \/ 4 | | | 1 \/ 4 \/ \/ 4 | |- - + ---------------------------------------- - ----------------|*|- - + ---------------- - --------------------------------------------|*|- - + ---------------- + --------------------------------------------|*|- - - ---------------- - ----------------------------------------| \ 4 2 2 / \ 4 2 2 / \ 4 2 2 / \ 4 2 2 /
$$\left(- \frac{1}{4} - \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} + \frac{\sqrt{\sqrt[3]{11} + \frac{9}{2} + \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}}}}{2}\right) \left(- \frac{1}{4} + \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} - \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}} + \sqrt[3]{11} + \frac{9}{2}}\right|}}{2}\right) \left(- \frac{1}{4} + \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} + \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}} + \sqrt[3]{11} + \frac{9}{2}}\right|}}{2}\right) \left(- \frac{\sqrt{\sqrt[3]{11} + \frac{9}{2} + \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}}}}{2} - \frac{1}{4} - \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2}\right)$$
=
/ ______________________________________ \ / ______________________________________ \ / ________________________________________\ / ________________________________________\
| / ______________ ______________ / ______________\| | / ______________ ______________ / ______________\| | ______________ / ______________\ / | ______________ | | | ______________ / ______________\ / | ______________ | |
| ___ / / 3 ____ / 3 ____\ 4 / 3 ____ | / 3 ____ || | ___ / / 3 ____ / 3 ____\ 4 / 3 ____ | / 3 ____ || |4 / 3 ____ | / 3 ____ | ___ / | / 3 ____ / 3 ____\| | |4 / 3 ____ | / 3 ____ | ___ / | / 3 ____ / 3 ____\| |
-\\/ 2 *\/ 5 + \/ 9 - 4*\/ 11 *\9 + 2*\/ 11 / + \/ 9 - 4*\/ 11 *\1 + \/ 9 - 4*\/ 11 //*\\/ 2 *\/ 5 + \/ 9 - 4*\/ 11 *\9 + 2*\/ 11 / - \/ 9 - 4*\/ 11 *\1 + \/ 9 - 4*\/ 11 //*\\/ 9 - 4*\/ 11 *\1 - \/ 9 - 4*\/ 11 / + I*\/ 2 *\/ |5 - \/ 9 - 4*\/ 11 *\9 + 2*\/ 11 /| /*\\/ 9 - 4*\/ 11 *\1 - \/ 9 - 4*\/ 11 / - I*\/ 2 *\/ |5 - \/ 9 - 4*\/ 11 *\9 + 2*\/ 11 /| /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 ____
2304 - 1024*\/ 11
$$- \frac{\left(\left(1 - \sqrt{9 - 4 \sqrt[3]{11}}\right) \sqrt[4]{9 - 4 \sqrt[3]{11}} - \sqrt{2} i \sqrt{\left|{- \sqrt{9 - 4 \sqrt[3]{11}} \left(2 \sqrt[3]{11} + 9\right) + 5}\right|}\right) \left(\left(1 - \sqrt{9 - 4 \sqrt[3]{11}}\right) \sqrt[4]{9 - 4 \sqrt[3]{11}} + \sqrt{2} i \sqrt{\left|{- \sqrt{9 - 4 \sqrt[3]{11}} \left(2 \sqrt[3]{11} + 9\right) + 5}\right|}\right) \left(- \sqrt[4]{9 - 4 \sqrt[3]{11}} \left(\sqrt{9 - 4 \sqrt[3]{11}} + 1\right) + \sqrt{2} \sqrt{\sqrt{9 - 4 \sqrt[3]{11}} \left(2 \sqrt[3]{11} + 9\right) + 5}\right) \left(\sqrt[4]{9 - 4 \sqrt[3]{11}} \left(\sqrt{9 - 4 \sqrt[3]{11}} + 1\right) + \sqrt{2} \sqrt{\sqrt{9 - 4 \sqrt[3]{11}} \left(2 \sqrt[3]{11} + 9\right) + 5}\right)}{2304 - 1024 \sqrt[3]{11}}$$
-(sqrt(2)*sqrt(5 + sqrt(9 - 4*11^(1/3))*(9 + 2*11^(1/3))) + (9 - 4*11^(1/3))^(1/4)*(1 + sqrt(9 - 4*11^(1/3))))*(sqrt(2)*sqrt(5 + sqrt(9 - 4*11^(1/3))*(9 + 2*11^(1/3))) - (9 - 4*11^(1/3))^(1/4)*(1 + sqrt(9 - 4*11^(1/3))))*((9 - 4*11^(1/3))^(1/4)*(1 - sqrt(9 - 4*11^(1/3))) + i*sqrt(2)*sqrt(Abs(5 - sqrt(9 - 4*11^(1/3))*(9 + 2*11^(1/3)))))*((9 - 4*11^(1/3))^(1/4)*(1 - sqrt(9 - 4*11^(1/3))) - i*sqrt(2)*sqrt(Abs(5 - sqrt(9 - 4*11^(1/3))*(9 + 2*11^(1/3)))))/(2304 - 1024*11^(1/3))
Respuesta rápida
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_________________________________
/ 9 3 ____ 5
/ - + \/ 11 + ------------------
/ 2 ____________ ____________
/ / 9 3 ____ / 9 3 ____
/ 4* / - - \/ 11 / - - \/ 11
1 \/ \/ 4 \/ 4
x1 = - - + ---------------------------------------- - ----------------
4 2 2
$$x_{1} = - \frac{1}{4} - \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} + \frac{\sqrt{\sqrt[3]{11} + \frac{9}{2} + \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}}}}{2}$$
___________________________________
/ |9 3 ____ 5 |
I* / |- + \/ 11 - ------------------|
____________ / |2 ____________|
/ 9 3 ____ / | / 9 3 ____ |
/ - - \/ 11 / | 4* / - - \/ 11 |
1 \/ 4 \/ | \/ 4 |
x2 = - - + ---------------- - --------------------------------------------
4 2 2
$$x_{2} = - \frac{1}{4} + \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} - \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}} + \sqrt[3]{11} + \frac{9}{2}}\right|}}{2}$$
___________________________________
/ |9 3 ____ 5 |
I* / |- + \/ 11 - ------------------|
____________ / |2 ____________|
/ 9 3 ____ / | / 9 3 ____ |
/ - - \/ 11 / | 4* / - - \/ 11 |
1 \/ 4 \/ | \/ 4 |
x3 = - - + ---------------- + --------------------------------------------
4 2 2
$$x_{3} = - \frac{1}{4} + \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2} + \frac{i \sqrt{\left|{- \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}} + \sqrt[3]{11} + \frac{9}{2}}\right|}}{2}$$
_________________________________
/ 9 3 ____ 5
/ - + \/ 11 + ------------------
____________ / 2 ____________
/ 9 3 ____ / / 9 3 ____
/ - - \/ 11 / 4* / - - \/ 11
1 \/ 4 \/ \/ 4
x4 = - - - ---------------- - ----------------------------------------
4 2 2
$$x_{4} = - \frac{\sqrt{\sqrt[3]{11} + \frac{9}{2} + \frac{5}{4 \sqrt{\frac{9}{4} - \sqrt[3]{11}}}}}{2} - \frac{1}{4} - \frac{\sqrt{\frac{9}{4} - \sqrt[3]{11}}}{2}$$
x4 = -sqrt(11^(1/3) + 9/2 + 5/(4*sqrt(9/4 - 11^(1/3))))/2 - 1/4 - sqrt(9/4 - 11^(1/3))/2
Respuesta numérica
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x1 = 1.57152850491772
x2 = -0.169346560162191 - 0.506266832479944*i
x3 = -0.169346560162191 + 0.506266832479944*i
x4 = -2.23283538459334
x4 = -2.23283538459334