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- La ecuación:
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
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Ecuación x^2-5x=0
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Ecuación x^2+4=5x
- Ecuación x^4-35*x^2-36=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- -17*x-15*y=-17
- -6*x-10*y=19
- -9*x+11*y=9
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Expresiones idénticas
- x^ dos *(x- veinticinco . novecientos veintidós)= tres . setecientos sesenta y siete * diez ^ tres
- x al cuadrado multiplicar por (x menos 25.922) es igual a 3.767 multiplicar por 10 al cubo
- x en el grado dos multiplicar por (x menos veinticinco . novecientos veintidós) es igual a tres . setecientos sesenta y siete multiplicar por diez en el grado tres
- x2*(x-25.922)=3.767*103
- x2*x-25.922=3.767*103
- x²*(x-25.922)=3.767*10³
- x en el grado 2*(x-25.922)=3.767*10 en el grado 3
- x^2(x-25.922)=3.76710^3
- x2(x-25.922)=3.767103
- x2x-25.922=3.767103
- x^2x-25.922=3.76710^3
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Expresiones semejantes
- x^2*(x+25.922)=3.767*10^3
x^2*(x-25.922)=3.767*10^3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 / 12961\ 3767*1000 x *|x - -----| = --------- \ 500 / 1000
$$x^{2} \left(x - \frac{12961}{500}\right) = \frac{1000 \cdot 3767}{1000}$$
Respuesta rápida
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________________________________________ / ________________________________________ \
/ ____________________ | / ____________________ |
/ 8534098759681 \/ 302623405259524905 | ___ / 8534098759681 \/ 302623405259524905 |
3 / ------------- + ---------------------- | \/ 3 *3 / ------------- + ---------------------- ___ |
12961 167987521 \/ 3375000000 225000 | \/ 3375000000 225000 167987521*\/ 3 |
x1 = ----- - ----------------------------------------------------- - --------------------------------------------- + I*|- --------------------------------------------------- + -----------------------------------------------------|
1500 ________________________________________ 2 | 2 ________________________________________|
/ ____________________ | / ____________________ |
/ 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905 |
4500000*3 / ------------- + ---------------------- | 4500000*3 / ------------- + ---------------------- |
\/ 3375000000 225000 \ \/ 3375000000 225000 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} - \frac{167987521}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} + \frac{167987521 \sqrt{3}}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}\right)$$
________________________________________ / ________________________________________ \
/ ____________________ | / ____________________ |
/ 8534098759681 \/ 302623405259524905 | ___ / 8534098759681 \/ 302623405259524905 |
3 / ------------- + ---------------------- |\/ 3 *3 / ------------- + ---------------------- ___ |
12961 167987521 \/ 3375000000 225000 | \/ 3375000000 225000 167987521*\/ 3 |
x2 = ----- - ----------------------------------------------------- - --------------------------------------------- + I*|--------------------------------------------------- - -----------------------------------------------------|
1500 ________________________________________ 2 | 2 ________________________________________|
/ ____________________ | / ____________________ |
/ 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905 |
4500000*3 / ------------- + ---------------------- | 4500000*3 / ------------- + ---------------------- |
\/ 3375000000 225000 \ \/ 3375000000 225000 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} - \frac{167987521}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + i \left(- \frac{167987521 \sqrt{3}}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2}\right)$$
________________________________________
/ ____________________
12961 / 8534098759681 \/ 302623405259524905 167987521
x3 = ----- + 3 / ------------- + ---------------------- + -----------------------------------------------------
1500 \/ 3375000000 225000 ________________________________________
/ ____________________
/ 8534098759681 \/ 302623405259524905
2250000*3 / ------------- + ----------------------
\/ 3375000000 225000
$$x_{3} = \frac{167987521}{2250000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}$$
x3 = 167987521/(2250000*(sqrt(302623405259524905)/225000 + 8534098759681/3375000000)^(1/3)) + 12961/1500 + (sqrt(302623405259524905)/225000 + 8534098759681/3375000000)^(1/3)
Suma y producto de raíces
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suma
________________________________________ / ________________________________________ \ ________________________________________ / ________________________________________ \
/ ____________________ | / ____________________ | / ____________________ | / ____________________ |
/ 8534098759681 \/ 302623405259524905 | ___ / 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905 | ___ / 8534098759681 \/ 302623405259524905 | ________________________________________
3 / ------------- + ---------------------- | \/ 3 *3 / ------------- + ---------------------- ___ | 3 / ------------- + ---------------------- |\/ 3 *3 / ------------- + ---------------------- ___ | / ____________________
12961 167987521 \/ 3375000000 225000 | \/ 3375000000 225000 167987521*\/ 3 | 12961 167987521 \/ 3375000000 225000 | \/ 3375000000 225000 167987521*\/ 3 | 12961 / 8534098759681 \/ 302623405259524905 167987521
----- - ----------------------------------------------------- - --------------------------------------------- + I*|- --------------------------------------------------- + -----------------------------------------------------| + ----- - ----------------------------------------------------- - --------------------------------------------- + I*|--------------------------------------------------- - -----------------------------------------------------| + ----- + 3 / ------------- + ---------------------- + -----------------------------------------------------
1500 ________________________________________ 2 | 2 ________________________________________| 1500 ________________________________________ 2 | 2 ________________________________________| 1500 \/ 3375000000 225000 ________________________________________
/ ____________________ | / ____________________ | / ____________________ | / ____________________ | / ____________________
/ 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905
4500000*3 / ------------- + ---------------------- | 4500000*3 / ------------- + ---------------------- | 4500000*3 / ------------- + ---------------------- | 4500000*3 / ------------- + ---------------------- | 2250000*3 / ------------- + ----------------------
\/ 3375000000 225000 \ \/ 3375000000 225000 / \/ 3375000000 225000 \ \/ 3375000000 225000 / \/ 3375000000 225000
$$\left(\frac{167987521}{2250000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} - \frac{167987521}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} + \frac{167987521 \sqrt{3}}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} - \frac{167987521}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + i \left(- \frac{167987521 \sqrt{3}}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2}\right)\right)\right)$$
=
/ ________________________________________ \ / ________________________________________ \
| / ____________________ | | / ____________________ |
| ___ / 8534098759681 \/ 302623405259524905 | | ___ / 8534098759681 \/ 302623405259524905 |
|\/ 3 *3 / ------------- + ---------------------- ___ | | \/ 3 *3 / ------------- + ---------------------- ___ |
12961 | \/ 3375000000 225000 167987521*\/ 3 | | \/ 3375000000 225000 167987521*\/ 3 |
----- + I*|--------------------------------------------------- - -----------------------------------------------------| + I*|- --------------------------------------------------- + -----------------------------------------------------|
500 | 2 ________________________________________| | 2 ________________________________________|
| / ____________________ | | / ____________________ |
| / 8534098759681 \/ 302623405259524905 | | / 8534098759681 \/ 302623405259524905 |
| 4500000*3 / ------------- + ---------------------- | | 4500000*3 / ------------- + ---------------------- |
\ \/ 3375000000 225000 / \ \/ 3375000000 225000 /
$$\frac{12961}{500} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} + \frac{167987521 \sqrt{3}}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}\right) + i \left(- \frac{167987521 \sqrt{3}}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2}\right)$$
producto
/ ________________________________________ / ________________________________________ \\ / ________________________________________ / ________________________________________ \\ | / ____________________ | / ____________________ || | / ____________________ | / ____________________ || | / 8534098759681 \/ 302623405259524905 | ___ / 8534098759681 \/ 302623405259524905 || | / 8534098759681 \/ 302623405259524905 | ___ / 8534098759681 \/ 302623405259524905 || / ________________________________________ \ | 3 / ------------- + ---------------------- | \/ 3 *3 / ------------- + ---------------------- ___ || | 3 / ------------- + ---------------------- |\/ 3 *3 / ------------- + ---------------------- ___ || | / ____________________ | |12961 167987521 \/ 3375000000 225000 | \/ 3375000000 225000 167987521*\/ 3 || |12961 167987521 \/ 3375000000 225000 | \/ 3375000000 225000 167987521*\/ 3 || |12961 / 8534098759681 \/ 302623405259524905 167987521 | |----- - ----------------------------------------------------- - --------------------------------------------- + I*|- --------------------------------------------------- + -----------------------------------------------------||*|----- - ----------------------------------------------------- - --------------------------------------------- + I*|--------------------------------------------------- - -----------------------------------------------------||*|----- + 3 / ------------- + ---------------------- + -----------------------------------------------------| | 1500 ________________________________________ 2 | 2 ________________________________________|| | 1500 ________________________________________ 2 | 2 ________________________________________|| | 1500 \/ 3375000000 225000 ________________________________________| | / ____________________ | / ____________________ || | / ____________________ | / ____________________ || | / ____________________ | | / 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905 || | / 8534098759681 \/ 302623405259524905 | / 8534098759681 \/ 302623405259524905 || | / 8534098759681 \/ 302623405259524905 | | 4500000*3 / ------------- + ---------------------- | 4500000*3 / ------------- + ---------------------- || | 4500000*3 / ------------- + ---------------------- | 4500000*3 / ------------- + ---------------------- || | 2250000*3 / ------------- + ---------------------- | \ \/ 3375000000 225000 \ \/ 3375000000 225000 // \ \/ 3375000000 225000 \ \/ 3375000000 225000 // \ \/ 3375000000 225000 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} - \frac{167987521}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + i \left(- \frac{167987521 \sqrt{3}}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} - \frac{167987521}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}{2} + \frac{167987521 \sqrt{3}}{4500000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}}\right)\right) \left(\frac{167987521}{2250000 \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}} + \frac{12961}{1500} + \sqrt[3]{\frac{\sqrt{302623405259524905}}{225000} + \frac{8534098759681}{3375000000}}\right)$$
=
3767
$$3767$$
3767
Respuesta numérica
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x1 = 30.0841680283678
x2 = -2.0810840141839 + 10.9947465479485*i
x3 = -2.0810840141839 - 10.9947465479485*i
x3 = -2.0810840141839 - 10.9947465479485*i