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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 9-7(x+3)=5-6x
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Ecuación 4x-5=3+2(x+1)
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Ecuación 6/(x-2)+5/x=3
- Expresar {x} en función de y en la ecuación:
- -14*x-12*y=-13
- -20*x+14*y=16
- -7*x+15*y=-11
- -14*x+5*y=3
- Derivada de:
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(x+3)^4
- Integral de d{x}:
- (x+3)^4
- Forma canónica:
- (x+3)^4
-
Expresiones idénticas
- (x+ uno)^ cuatro +(x+ dos)^ cuatro =(x+ tres)^ cuatro
- (x más 1) en el grado 4 más (x más 2) en el grado 4 es igual a (x más 3) en el grado 4
- (x más uno) en el grado cuatro más (x más dos) en el grado cuatro es igual a (x más tres) en el grado cuatro
- (x+1)4+(x+2)4=(x+3)4
- x+14+x+24=x+34
- (x+1)⁴+(x+2)⁴=(x+3)⁴
- x+1^4+x+2^4=x+3^4
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Expresiones semejantes
- (x+1)^4+(x-2)^4=(x+3)^4
- (x+1)^4+(x+2)^4=(x-3)^4
- (x+1)^4-(x+2)^4=(x+3)^4
- (x-1)^4+(x+2)^4=(x+3)^4
(x+1)^4+(x+2)^4=(x+3)^4 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 4 4 (x + 1) + (x + 2) = (x + 3)
$$\left(x + 1\right)^{4} + \left(x + 2\right)^{4} = \left(x + 3\right)^{4}$$
Respuesta rápida
[src]
x1 = -2
$$x_{1} = -2$$
_______________ / _______________ \
/ _____ | / _____ ___ |
2 / 155 \/ 849 16 | ___ / 155 \/ 849 16*\/ 3 |
x2 = - - 3 / --- + ------- - ---------------------- + I*|- \/ 3 *3 / --- + ------- + ----------------------|
3 \/ 54 18 _______________ | \/ 54 18 _______________|
/ _____ | / _____ |
/ 155 \/ 849 | / 155 \/ 849 |
9*3 / --- + ------- | 9*3 / --- + ------- |
\/ 54 18 \ \/ 54 18 /
$$x_{2} = - \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} - \frac{16}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \frac{2}{3} + i \left(- \sqrt{3} \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} + \frac{16 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}}\right)$$
_______________ / _______________ \
/ _____ | / _____ ___ |
2 / 155 \/ 849 16 | ___ / 155 \/ 849 16*\/ 3 |
x3 = - - 3 / --- + ------- - ---------------------- + I*|\/ 3 *3 / --- + ------- - ----------------------|
3 \/ 54 18 _______________ | \/ 54 18 _______________|
/ _____ | / _____ |
/ 155 \/ 849 | / 155 \/ 849 |
9*3 / --- + ------- | 9*3 / --- + ------- |
\/ 54 18 \ \/ 54 18 /
$$x_{3} = - \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} - \frac{16}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \frac{2}{3} + i \left(- \frac{16 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \sqrt{3} \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}\right)$$
_______________
/ _____
2 / 155 \/ 849 32
x4 = - + 2*3 / --- + ------- + ----------------------
3 \/ 54 18 _______________
/ _____
/ 155 \/ 849
9*3 / --- + -------
\/ 54 18
$$x_{4} = \frac{2}{3} + \frac{32}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + 2 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}$$
x4 = 2/3 + 32/(9*(sqrt(849)/18 + 155/54)^(1/3)) + 2*(sqrt(849)/18 + 155/54)^(1/3)
Suma y producto de raíces
[src]
suma
_______________ / _______________ \ _______________ / _______________ \ _______________
/ _____ | / _____ ___ | / _____ | / _____ ___ | / _____
2 / 155 \/ 849 16 | ___ / 155 \/ 849 16*\/ 3 | 2 / 155 \/ 849 16 | ___ / 155 \/ 849 16*\/ 3 | 2 / 155 \/ 849 32
-2 + - - 3 / --- + ------- - ---------------------- + I*|- \/ 3 *3 / --- + ------- + ----------------------| + - - 3 / --- + ------- - ---------------------- + I*|\/ 3 *3 / --- + ------- - ----------------------| + - + 2*3 / --- + ------- + ----------------------
3 \/ 54 18 _______________ | \/ 54 18 _______________| 3 \/ 54 18 _______________ | \/ 54 18 _______________| 3 \/ 54 18 _______________
/ _____ | / _____ | / _____ | / _____ | / _____
/ 155 \/ 849 | / 155 \/ 849 | / 155 \/ 849 | / 155 \/ 849 | / 155 \/ 849
9*3 / --- + ------- | 9*3 / --- + ------- | 9*3 / --- + ------- | 9*3 / --- + ------- | 9*3 / --- + -------
\/ 54 18 \ \/ 54 18 / \/ 54 18 \ \/ 54 18 / \/ 54 18
$$\left(\frac{2}{3} + \frac{32}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + 2 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}\right) + \left(\left(-2 + \left(- \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} - \frac{16}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \frac{2}{3} + i \left(- \sqrt{3} \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} + \frac{16 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}}\right)\right)\right) + \left(- \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} - \frac{16}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \frac{2}{3} + i \left(- \frac{16 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \sqrt{3} \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}\right)\right)\right)$$
=
/ _______________ \ / _______________ \ | / _____ ___ | | / _____ ___ | | ___ / 155 \/ 849 16*\/ 3 | | ___ / 155 \/ 849 16*\/ 3 | I*|\/ 3 *3 / --- + ------- - ----------------------| + I*|- \/ 3 *3 / --- + ------- + ----------------------| | \/ 54 18 _______________| | \/ 54 18 _______________| | / _____ | | / _____ | | / 155 \/ 849 | | / 155 \/ 849 | | 9*3 / --- + ------- | | 9*3 / --- + ------- | \ \/ 54 18 / \ \/ 54 18 /
$$i \left(- \sqrt{3} \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} + \frac{16 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}}\right) + i \left(- \frac{16 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \sqrt{3} \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}\right)$$
producto
/ _______________ / _______________ \\ / _______________ / _______________ \\ / _______________ \ | / _____ | / _____ ___ || | / _____ | / _____ ___ || | / _____ | |2 / 155 \/ 849 16 | ___ / 155 \/ 849 16*\/ 3 || |2 / 155 \/ 849 16 | ___ / 155 \/ 849 16*\/ 3 || |2 / 155 \/ 849 32 | -2*|- - 3 / --- + ------- - ---------------------- + I*|- \/ 3 *3 / --- + ------- + ----------------------||*|- - 3 / --- + ------- - ---------------------- + I*|\/ 3 *3 / --- + ------- - ----------------------||*|- + 2*3 / --- + ------- + ----------------------| |3 \/ 54 18 _______________ | \/ 54 18 _______________|| |3 \/ 54 18 _______________ | \/ 54 18 _______________|| |3 \/ 54 18 _______________| | / _____ | / _____ || | / _____ | / _____ || | / _____ | | / 155 \/ 849 | / 155 \/ 849 || | / 155 \/ 849 | / 155 \/ 849 || | / 155 \/ 849 | | 9*3 / --- + ------- | 9*3 / --- + ------- || | 9*3 / --- + ------- | 9*3 / --- + ------- || | 9*3 / --- + ------- | \ \/ 54 18 \ \/ 54 18 // \ \/ 54 18 \ \/ 54 18 // \ \/ 54 18 /
$$\left(- \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} - \frac{16}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \frac{2}{3} + i \left(- \frac{16 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \sqrt{3} \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}\right)\right) \left(- 2 \left(- \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} - \frac{16}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + \frac{2}{3} + i \left(- \sqrt{3} \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}} + \frac{16 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}}\right)\right)\right) \left(\frac{2}{3} + \frac{32}{9 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}} + 2 \sqrt[3]{\frac{\sqrt{849}}{18} + \frac{155}{54}}\right)$$
=
-64
$$-64$$
-64
Respuesta numérica
[src]
x1 = -2.06064702755414 + 0.990649598354402*i
x2 = 6.12129405510828
x3 = -2.0
x4 = -2.06064702755414 - 0.990649598354402*i
x4 = -2.06064702755414 - 0.990649598354402*i
Gráfico