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- La ecuación:
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Ecuación 6*x^2+x-7=0
- Ecuación z^5+32=0
-
Ecuación 2-5(3+2x)=17
-
Ecuación (6*x+8)/2+5=5*x/3
- Expresar {x} en función de y en la ecuación:
- 16*x-17*y=-15
- -10*x-12*y=-10
- 4*x+12*y=-11
- -16*x-9*y=-1
-
Expresiones idénticas
- x*(ciento quince +x)*(x- diez)*(doscientos sesenta y nueve +x)-(setenta y uno -x)*(trescientos cincuenta y siete -x)*(setenta y dos -x)*(ciento ochenta y seis -x)= cero
- x multiplicar por (115 más x) multiplicar por (x menos 10) multiplicar por (269 más x) menos (71 menos x) multiplicar por (357 menos x) multiplicar por (72 menos x) multiplicar por (186 menos x) es igual a 0
- x multiplicar por (ciento quince más x) multiplicar por (x menos diez) multiplicar por (doscientos sesenta y nueve más x) menos (setenta y uno menos x) multiplicar por (trescientos cincuenta y siete menos x) multiplicar por (setenta y dos menos x) multiplicar por (ciento ochenta y seis menos x) es igual a cero
- x(115+x)(x-10)(269+x)-(71-x)(357-x)(72-x)(186-x)=0
- x115+xx-10269+x-71-x357-x72-x186-x=0
- x*(115+x)*(x-10)*(269+x)-(71-x)*(357-x)*(72-x)*(186-x)=O
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Expresiones semejantes
- x*(115-x)*(x-10)*(269+x)-(71-x)*(357-x)*(72-x)*(186-x)=0
- x*(115+x)*(x+10)*(269+x)-(71-x)*(357-x)*(72-x)*(186-x)=0
- x*(115+x)*(x-10)*(269+x)-(71+x)*(357-x)*(72-x)*(186-x)=0
- x*(115+x)*(x-10)*(269+x)+(71-x)*(357-x)*(72-x)*(186-x)=0
- x*(115+x)*(x-10)*(269+x)-(71-x)*(357-x)*(72+x)*(186-x)=0
- x*(115+x)*(x-10)*(269+x)-(71-x)*(357-x)*(72-x)*(186+x)=0
- x*(115+x)*(x-10)*(269-x)-(71-x)*(357-x)*(72-x)*(186-x)=0
- x*(115+x)*(x-10)*(269+x)-(71-x)*(357+x)*(72-x)*(186-x)=0
x*(115+x)*(x-10)*(269+x)-(71-x)*(357-x)*(72-x)*(186-x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
x*(115 + x)*(x - 10)*(269 + x) - (71 - x)*(357 - x)*(72 - x)*(186 - x) = 0
$$x \left(x + 115\right) \left(x - 10\right) \left(x + 269\right) - \left(71 - x\right) \left(357 - x\right) \left(72 - x\right) \left(186 - x\right) = 0$$
Respuesta rápida
[src]
___________________________________________ / ___________________________________________\
/ _______________________ | / _______________________ |
/ 43809864283 2*\/ 132924228340199690402 | ___ / 43809864283 2*\/ 132924228340199690402 |
3 / ----------- + --------------------------- | ___ \/ 3 *3 / ----------- + --------------------------- |
30517 \/ 502459875 210675 1446150671 | 1446150671*\/ 3 \/ 502459875 210675 |
x1 = ----- - ------------------------------------------------ + -------------------------------------------------------- + I*|- -------------------------------------------------------- - ------------------------------------------------------|
795 2 ___________________________________________ | ___________________________________________ 2 |
/ _______________________ | / _______________________ |
/ 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402 |
1264050*3 / ----------- + --------------------------- | 1264050*3 / ----------- + --------------------------- |
\/ 502459875 210675 \ \/ 502459875 210675 /
$$x_{1} = - \frac{\sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} + \frac{1446150671}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} - \frac{1446150671 \sqrt{3}}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}\right)$$
___________________________________________ / ___________________________________________ \
/ _______________________ | / _______________________ |
/ 43809864283 2*\/ 132924228340199690402 | ___ / 43809864283 2*\/ 132924228340199690402 |
3 / ----------- + --------------------------- |\/ 3 *3 / ----------- + --------------------------- ___ |
30517 \/ 502459875 210675 1446150671 | \/ 502459875 210675 1446150671*\/ 3 |
x2 = ----- - ------------------------------------------------ + -------------------------------------------------------- + I*|------------------------------------------------------ + --------------------------------------------------------|
795 2 ___________________________________________ | 2 ___________________________________________|
/ _______________________ | / _______________________ |
/ 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402 |
1264050*3 / ----------- + --------------------------- | 1264050*3 / ----------- + --------------------------- |
\/ 502459875 210675 \ \/ 502459875 210675 /
$$x_{2} = - \frac{\sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} + \frac{1446150671}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + i \left(\frac{1446150671 \sqrt{3}}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{\sqrt{3} \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2}\right)$$
___________________________________________
/ _______________________
30517 / 43809864283 2*\/ 132924228340199690402 1446150671
x3 = ----- + 3 / ----------- + --------------------------- - -------------------------------------------------------
795 \/ 502459875 210675 ___________________________________________
/ _______________________
/ 43809864283 2*\/ 132924228340199690402
632025*3 / ----------- + ---------------------------
\/ 502459875 210675
$$x_{3} = - \frac{1446150671}{632025 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}$$
x3 = -1446150671/(632025*(43809864283/502459875 + 2*sqrt(132924228340199690402)/210675)^(1/3)) + 30517/795 + (43809864283/502459875 + 2*sqrt(132924228340199690402)/210675)^(1/3)
Suma y producto de raíces
[src]
suma
___________________________________________ / ___________________________________________\ ___________________________________________ / ___________________________________________ \
/ _______________________ | / _______________________ | / _______________________ | / _______________________ |
/ 43809864283 2*\/ 132924228340199690402 | ___ / 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402 | ___ / 43809864283 2*\/ 132924228340199690402 | ___________________________________________
3 / ----------- + --------------------------- | ___ \/ 3 *3 / ----------- + --------------------------- | 3 / ----------- + --------------------------- |\/ 3 *3 / ----------- + --------------------------- ___ | / _______________________
30517 \/ 502459875 210675 1446150671 | 1446150671*\/ 3 \/ 502459875 210675 | 30517 \/ 502459875 210675 1446150671 | \/ 502459875 210675 1446150671*\/ 3 | 30517 / 43809864283 2*\/ 132924228340199690402 1446150671
----- - ------------------------------------------------ + -------------------------------------------------------- + I*|- -------------------------------------------------------- - ------------------------------------------------------| + ----- - ------------------------------------------------ + -------------------------------------------------------- + I*|------------------------------------------------------ + --------------------------------------------------------| + ----- + 3 / ----------- + --------------------------- - -------------------------------------------------------
795 2 ___________________________________________ | ___________________________________________ 2 | 795 2 ___________________________________________ | 2 ___________________________________________| 795 \/ 502459875 210675 ___________________________________________
/ _______________________ | / _______________________ | / _______________________ | / _______________________ | / _______________________
/ 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402
1264050*3 / ----------- + --------------------------- | 1264050*3 / ----------- + --------------------------- | 1264050*3 / ----------- + --------------------------- | 1264050*3 / ----------- + --------------------------- | 632025*3 / ----------- + ---------------------------
\/ 502459875 210675 \ \/ 502459875 210675 / \/ 502459875 210675 \ \/ 502459875 210675 / \/ 502459875 210675
$$\left(- \frac{1446150671}{632025 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} + \frac{1446150671}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} - \frac{1446150671 \sqrt{3}}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} + \frac{1446150671}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + i \left(\frac{1446150671 \sqrt{3}}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{\sqrt{3} \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2}\right)\right)\right)$$
=
/ ___________________________________________ \ / ___________________________________________\
| / _______________________ | | / _______________________ |
| ___ / 43809864283 2*\/ 132924228340199690402 | | ___ / 43809864283 2*\/ 132924228340199690402 |
|\/ 3 *3 / ----------- + --------------------------- ___ | | ___ \/ 3 *3 / ----------- + --------------------------- |
30517 | \/ 502459875 210675 1446150671*\/ 3 | | 1446150671*\/ 3 \/ 502459875 210675 |
----- + I*|------------------------------------------------------ + --------------------------------------------------------| + I*|- -------------------------------------------------------- - ------------------------------------------------------|
265 | 2 ___________________________________________| | ___________________________________________ 2 |
| / _______________________ | | / _______________________ |
| / 43809864283 2*\/ 132924228340199690402 | | / 43809864283 2*\/ 132924228340199690402 |
| 1264050*3 / ----------- + --------------------------- | | 1264050*3 / ----------- + --------------------------- |
\ \/ 502459875 210675 / \ \/ 502459875 210675 /
$$\frac{30517}{265} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} - \frac{1446150671 \sqrt{3}}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}\right) + i \left(\frac{1446150671 \sqrt{3}}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{\sqrt{3} \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2}\right)$$
producto
/ ___________________________________________ / ___________________________________________\\ / ___________________________________________ / ___________________________________________ \\ | / _______________________ | / _______________________ || | / _______________________ | / _______________________ || | / 43809864283 2*\/ 132924228340199690402 | ___ / 43809864283 2*\/ 132924228340199690402 || | / 43809864283 2*\/ 132924228340199690402 | ___ / 43809864283 2*\/ 132924228340199690402 || / ___________________________________________ \ | 3 / ----------- + --------------------------- | ___ \/ 3 *3 / ----------- + --------------------------- || | 3 / ----------- + --------------------------- |\/ 3 *3 / ----------- + --------------------------- ___ || | / _______________________ | |30517 \/ 502459875 210675 1446150671 | 1446150671*\/ 3 \/ 502459875 210675 || |30517 \/ 502459875 210675 1446150671 | \/ 502459875 210675 1446150671*\/ 3 || |30517 / 43809864283 2*\/ 132924228340199690402 1446150671 | |----- - ------------------------------------------------ + -------------------------------------------------------- + I*|- -------------------------------------------------------- - ------------------------------------------------------||*|----- - ------------------------------------------------ + -------------------------------------------------------- + I*|------------------------------------------------------ + --------------------------------------------------------||*|----- + 3 / ----------- + --------------------------- - -------------------------------------------------------| | 795 2 ___________________________________________ | ___________________________________________ 2 || | 795 2 ___________________________________________ | 2 ___________________________________________|| | 795 \/ 502459875 210675 ___________________________________________| | / _______________________ | / _______________________ || | / _______________________ | / _______________________ || | / _______________________ | | / 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402 || | / 43809864283 2*\/ 132924228340199690402 | / 43809864283 2*\/ 132924228340199690402 || | / 43809864283 2*\/ 132924228340199690402 | | 1264050*3 / ----------- + --------------------------- | 1264050*3 / ----------- + --------------------------- || | 1264050*3 / ----------- + --------------------------- | 1264050*3 / ----------- + --------------------------- || | 632025*3 / ----------- + --------------------------- | \ \/ 502459875 210675 \ \/ 502459875 210675 // \ \/ 502459875 210675 \ \/ 502459875 210675 // \ \/ 502459875 210675 /
$$\left(- \frac{\sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} + \frac{1446150671}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + i \left(\frac{1446150671 \sqrt{3}}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{\sqrt{3} \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} + \frac{1446150671}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}{2} - \frac{1446150671 \sqrt{3}}{1264050 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}}\right)\right) \left(- \frac{1446150671}{632025 \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}} + \frac{30517}{795} + \sqrt[3]{\frac{43809864283}{502459875} + \frac{2 \sqrt{132924228340199690402}}{210675}}\right)$$
=
84861756 -------- 265
$$\frac{84861756}{265}$$
84861756/265
Respuesta numérica
[src]
x1 = 38.3734615854279 - 82.8514828567359*i
x2 = 38.3734615854279 + 82.8514828567359*i
x3 = 38.411567395182
x3 = 38.411567395182