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- La ecuación:
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Ecuación 6*x^2+x-7=0
-
Ecuación 2-5(3+2x)=17
-
Ecuación (6*x+8)/2+5=5*x/3
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Ecuación 2+3x=−2x−13
- Expresar {x} en función de y en la ecuación:
- 6*x+4*y=15
- -4*x+4*y=-9
- 3*x-12*y=-14
- 1*x+4*y=-16
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Expresiones idénticas
- (x- cuatro)(x^ dos +16x+ treinta y dos)= trece (x+ ocho)
- (x menos 4)(x al cuadrado más 16x más 32) es igual a 13(x más 8)
- (x menos cuatro)(x en el grado dos más 16x más treinta y dos) es igual a trece (x más ocho)
- (x-4)(x2+16x+32)=13(x+8)
- x-4x2+16x+32=13x+8
- (x-4)(x²+16x+32)=13(x+8)
- (x-4)(x en el grado 2+16x+32)=13(x+8)
- x-4x^2+16x+32=13x+8
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Expresiones semejantes
- (x-4)(x^2+16x-32)=13(x+8)
- 13x+8=27ч+18
- (x-4)(x^2+16x+32)=13(x-8)
- (x+4)(x^2+16x+32)=13(x+8)
- (x-4)(x^2-16x+32)=13(x+8)
- (x-4)*(x^2-16x+64)=13*(x+8)
- 13⋅(5x−8)−5⋅(13x+8)=−144
(x-4)(x^2+16x+32)=13(x+8) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \ (x - 4)*\x + 16*x + 32/ = 13*(x + 8)
$$\left(x - 4\right) \left(\left(x^{2} + 16 x\right) + 32\right) = 13 \left(x + 8\right)$$
Respuesta rápida
[src]
/ / / _______\\ / / _______\\\ / / _______\\ / / _______\\
| | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||
| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /|
| \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = -4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- + ---------------------------| + --------------------------- - ---------------------------
| _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2
|3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || |
|\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| |
\ \ 2 2 // \ \ \ 2 2 // /
$$x_{1} = -4 - \frac{\sqrt{93} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + \frac{\sqrt{31} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + i \left(- 93 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + \frac{\sqrt{31} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{93} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2}\right)$$
/ / / _______\\ / / _______\\\ / / _______\\ / / _______\\
| | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||
| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /|
| \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = -4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- - ---------------------------| + --------------------------- + ---------------------------
| _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2
|3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || |
|\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| |
\ \ 2 2 // \ \ \ 2 2 // /
$$x_{2} = -4 + \frac{\sqrt{93} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{31} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + i \left(- \frac{\sqrt{93} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{31} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)}\right)$$
_______________________
3 / _______
93 \/ 1026 + 27*I*\/ 28347
x3 = -4 - -------------------------- - --------------------------
_______________________ 3
3 / _______
\/ 1026 + 27*I*\/ 28347
$$x_{3} = -4 - \frac{\sqrt[3]{1026 + 27 \sqrt{28347} i}}{3} - \frac{93}{\sqrt[3]{1026 + 27 \sqrt{28347} i}}$$
x3 = -4 - (1026 + 27*sqrt(28347)*i)^(1/3)/3 - 93/(1026 + 27*sqrt(28347)*i)^(1/3)
Suma y producto de raíces
[src]
suma
/ / / _______\\ / / _______\\\ / / _______\\ / / _______\\ / / / _______\\ / / _______\\\ / / _______\\ / / _______\\
| | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 || | | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||
| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------|| | |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /| | ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /| _______________________
| \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------| | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------| 3 / _______
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / 93 \/ 1026 + 27*I*\/ 28347
-4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- + ---------------------------| + --------------------------- - --------------------------- + -4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- - ---------------------------| + --------------------------- + --------------------------- + -4 - -------------------------- - --------------------------
| _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2 | _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2 _______________________ 3
|3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | 3 / _______
|\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | \/ 1026 + 27*I*\/ 28347
\ \ 2 2 // \ \ \ 2 2 // / \ \ 2 2 // \ \ \ 2 2 // /
$$\left(\left(-4 + \frac{\sqrt{93} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{31} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + i \left(- \frac{\sqrt{93} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{31} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)}\right)\right) + \left(-4 - \frac{\sqrt{93} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + \frac{\sqrt{31} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + i \left(- 93 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + \frac{\sqrt{31} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{93} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2}\right)\right)\right) + \left(-4 - \frac{\sqrt[3]{1026 + 27 \sqrt{28347} i}}{3} - \frac{93}{\sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)$$
=
/ / / _______\\ / / _______\\\ / / / _______\\ / / _______\\\
| | |\/ 28347 || | |\/ 28347 ||| | | |\/ 28347 || | |\/ 28347 |||
| |atan|---------|| |atan|---------||| | |atan|---------|| |atan|---------||| / / _______\\
_______________________ | ____ | \ 38 /| ____ | \ 38 /|| | ____ | \ 38 /| ____ | \ 38 /|| | |\/ 28347 ||
3 / _______ | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| |atan|---------||
93 / 1 \ / 1 \ \/ 1026 + 27*I*\/ 28347 | / 1 \ \ 3 / \ 3 /| | / 1 \ \ 3 / \ 3 /| ____ | \ 38 /|
-12 - -------------------------- - 93*re|------------------------------------------| - 93*re|------------------------------------------| - -------------------------- + I*|- 93*im|------------------------------------------| + --------------------------- - ---------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- + ---------------------------| + \/ 31 *cos|---------------|
_______________________ | _______________________ / ___\| | _______________________ / ___\| 3 | | _______________________ / ___\| 2 2 | | | _______________________ / ___\| 2 2 | \ 3 /
3 / _______ |3 / _______ | 1 I*\/ 3 || |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | | |3 / _______ | 1 I*\/ 3 || |
\/ 1026 + 27*I*\/ 28347 |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| |
\ \ 2 2 // \ \ 2 2 // \ \ \ 2 2 // / \ \ \ 2 2 // /
$$-12 - 93 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} - 93 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + \sqrt{31} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)} - \frac{\sqrt[3]{1026 + 27 \sqrt{28347} i}}{3} + i \left(- 93 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + \frac{\sqrt{31} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{93} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2}\right) + i \left(- \frac{\sqrt{93} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{31} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)}\right) - \frac{93}{\sqrt[3]{1026 + 27 \sqrt{28347} i}}$$
producto
/ / / / _______\\ / / _______\\\ / / _______\\ / / _______\\\ / / / / _______\\ / / _______\\\ / / _______\\ / / _______\\\ | | | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||| | | | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||| | | |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||| | | |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||| | | ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /|| | | ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /|| / _______________________\ | | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------|| | | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------|| | 3 / _______ | | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | 93 \/ 1026 + 27*I*\/ 28347 | |-4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- + ---------------------------| + --------------------------- - ---------------------------|*|-4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- - ---------------------------| + --------------------------- + ---------------------------|*|-4 - -------------------------- - --------------------------| | | _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2 | | | _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2 | | _______________________ 3 | | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | | | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | | | 3 / _______ | | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | | | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | | \ \/ 1026 + 27*I*\/ 28347 / \ \ \ 2 2 // \ \ \ 2 2 // / / \ \ \ 2 2 // \ \ \ 2 2 // / /
$$\left(-4 - \frac{\sqrt{93} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + \frac{\sqrt{31} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + i \left(- 93 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + \frac{\sqrt{31} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{93} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2}\right)\right) \left(-4 + \frac{\sqrt{93} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{31} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)} + i \left(- \frac{\sqrt{93} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} + \frac{\sqrt{31} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}}{2} - 93 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)}\right)\right) \left(-4 - \frac{\sqrt[3]{1026 + 27 \sqrt{28347} i}}{3} - \frac{93}{\sqrt[3]{1026 + 27 \sqrt{28347} i}}\right)$$
=
/ / / _______\\ / / _______\\\
| | |\/ 28347 || | |\/ 28347 |||
/ __________________ / __________________\\ | |2*atan|---------|| |atan|---------|||
| 3 / _______ | 3 / _______ || | | \ 38 /| ____ | \ 38 /||
\31 + \/ 38 + I*\/ 28347 *\4 + \/ 38 + I*\/ 28347 //*|15 - 62*cos|-----------------| + 8*\/ 31 *cos|---------------||
\ \ 3 / \ 3 //
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__________________
3 / _______
\/ 38 + I*\/ 28347
$$\frac{\left(31 + \left(4 + \sqrt[3]{38 + \sqrt{28347} i}\right) \sqrt[3]{38 + \sqrt{28347} i}\right) \left(- 62 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)} + 15 + 8 \sqrt{31} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{28347}}{38} \right)}}{3} \right)}\right)}{\sqrt[3]{38 + \sqrt{28347} i}}$$
(31 + (38 + i*sqrt(28347))^(1/3)*(4 + (38 + i*sqrt(28347))^(1/3)))*(15 - 62*cos(2*atan(sqrt(28347)/38)/3) + 8*sqrt(31)*cos(atan(sqrt(28347)/38)/3))/(38 + i*sqrt(28347))^(1/3)
Respuesta numérica
[src]
x1 = -3.17679727084418
x2 = -14.0288646421446
x3 = 5.20566191298878
x3 = 5.20566191298878