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- La ecuación:
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Ecuación x+(x/4)=-5
- Ecuación z^4-81=0
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Ecuación z^3=8
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Ecuación x^3+x^2-2=0
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 16*x-11*y=13
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Expresiones idénticas
- (x+ seis)(x+ seis)(x+ tres)- tres = cero
- (x más 6)(x más 6)(x más 3) menos 3 es igual a 0
- (x más seis)(x más seis)(x más tres) menos tres es igual a cero
- x+6x+6x+3-3=0
- (x+6)(x+6)(x+3)-3=O
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Expresiones semejantes
- (x+6)(x+6)(x+3)+3=0
- (x+6)(x+6)(x-3)-3=0
- (x-6)(x+6)(x+3)-3=0
- (x+6)(x-6)(x+3)-3=0
(x+6)(x+6)(x+3)-3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
(x + 6)*(x + 6)*(x + 3) - 3 = 0
$$\left(x + 6\right) \left(x + 6\right) \left(x + 3\right) - 3 = 0$$
Suma y producto de raíces
[src]
suma
____________ / ____________\ ____________ / ____________ \
/ ____ | / ____ | / ____ | / ____ |
/ 5 \/ 21 | ___ / 5 \/ 21 | / 5 \/ 21 | ___ / 5 \/ 21 | ____________
3 / - + ------ | ___ \/ 3 *3 / - + ------ | 3 / - + ------ |\/ 3 *3 / - + ------ ___ | / ____
1 \/ 2 2 | \/ 3 \/ 2 2 | 1 \/ 2 2 | \/ 2 2 \/ 3 | 1 / 5 \/ 21
-5 - ------------------- - ----------------- + I*|------------------- - -----------------------| + -5 - ------------------- - ----------------- + I*|----------------------- - -------------------| + -5 + ----------------- + 3 / - + ------
____________ 2 | ____________ 2 | ____________ 2 | 2 ____________| ____________ \/ 2 2
/ ____ | / ____ | / ____ | / ____ | / ____
/ 5 \/ 21 | / 5 \/ 21 | / 5 \/ 21 | / 5 \/ 21 | / 5 \/ 21
2*3 / - + ------ |2*3 / - + ------ | 2*3 / - + ------ | 2*3 / - + ------ | 3 / - + ------
\/ 2 2 \ \/ 2 2 / \/ 2 2 \ \/ 2 2 / \/ 2 2
$$\left(-5 + \frac{1}{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}\right) + \left(\left(-5 - \frac{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}\right)\right) + \left(-5 - \frac{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2}\right)\right)\right)$$
=
/ ____________\ / ____________ \
| / ____ | | / ____ |
| ___ / 5 \/ 21 | | ___ / 5 \/ 21 |
| ___ \/ 3 *3 / - + ------ | |\/ 3 *3 / - + ------ ___ |
| \/ 3 \/ 2 2 | | \/ 2 2 \/ 3 |
-15 + I*|------------------- - -----------------------| + I*|----------------------- - -------------------|
| ____________ 2 | | 2 ____________|
| / ____ | | / ____ |
| / 5 \/ 21 | | / 5 \/ 21 |
|2*3 / - + ------ | | 2*3 / - + ------ |
\ \/ 2 2 / \ \/ 2 2 /
$$-15 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}\right) + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2}\right)$$
producto
/ ____________ / ____________\\ / ____________ / ____________ \\ | / ____ | / ____ || | / ____ | / ____ || | / 5 \/ 21 | ___ / 5 \/ 21 || | / 5 \/ 21 | ___ / 5 \/ 21 || / ____________\ | 3 / - + ------ | ___ \/ 3 *3 / - + ------ || | 3 / - + ------ |\/ 3 *3 / - + ------ ___ || | / ____ | | 1 \/ 2 2 | \/ 3 \/ 2 2 || | 1 \/ 2 2 | \/ 2 2 \/ 3 || | 1 / 5 \/ 21 | |-5 - ------------------- - ----------------- + I*|------------------- - -----------------------||*|-5 - ------------------- - ----------------- + I*|----------------------- - -------------------||*|-5 + ----------------- + 3 / - + ------ | | ____________ 2 | ____________ 2 || | ____________ 2 | 2 ____________|| | ____________ \/ 2 2 | | / ____ | / ____ || | / ____ | / ____ || | / ____ | | / 5 \/ 21 | / 5 \/ 21 || | / 5 \/ 21 | / 5 \/ 21 || | / 5 \/ 21 | | 2*3 / - + ------ |2*3 / - + ------ || | 2*3 / - + ------ | 2*3 / - + ------ || | 3 / - + ------ | \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 /
$$\left(-5 - \frac{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2}\right)\right) \left(-5 - \frac{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}\right)\right) \left(-5 + \frac{1}{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}\right)$$
=
-105
$$-105$$
-105
Respuesta rápida
[src]
____________ / ____________\
/ ____ | / ____ |
/ 5 \/ 21 | ___ / 5 \/ 21 |
3 / - + ------ | ___ \/ 3 *3 / - + ------ |
1 \/ 2 2 | \/ 3 \/ 2 2 |
x1 = -5 - ------------------- - ----------------- + I*|------------------- - -----------------------|
____________ 2 | ____________ 2 |
/ ____ | / ____ |
/ 5 \/ 21 | / 5 \/ 21 |
2*3 / - + ------ |2*3 / - + ------ |
\/ 2 2 \ \/ 2 2 /
$$x_{1} = -5 - \frac{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}\right)$$
____________ / ____________ \
/ ____ | / ____ |
/ 5 \/ 21 | ___ / 5 \/ 21 |
3 / - + ------ |\/ 3 *3 / - + ------ ___ |
1 \/ 2 2 | \/ 2 2 \/ 3 |
x2 = -5 - ------------------- - ----------------- + I*|----------------------- - -------------------|
____________ 2 | 2 ____________|
/ ____ | / ____ |
/ 5 \/ 21 | / 5 \/ 21 |
2*3 / - + ------ | 2*3 / - + ------ |
\/ 2 2 \ \/ 2 2 /
$$x_{2} = -5 - \frac{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}}{2}\right)$$
____________
/ ____
1 / 5 \/ 21
x3 = -5 + ----------------- + 3 / - + ------
____________ \/ 2 2
/ ____
/ 5 \/ 21
3 / - + ------
\/ 2 2
$$x_{3} = -5 + \frac{1}{\sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}} + \sqrt[3]{\frac{\sqrt{21}}{2} + \frac{5}{2}}$$
x3 = -5 + (sqrt(21)/2 + 5/2)^(-1/3) + (sqrt(21)/2 + 5/2)^(1/3)
Respuesta numérica
[src]
x1 = -6.1395093930833 - 0.946279541560099*i
x2 = -2.72098121383341
x3 = -6.1395093930833 + 0.946279541560099*i
x3 = -6.1395093930833 + 0.946279541560099*i