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- La ecuación:
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Ecuación 3^x=7
- Ecuación x+y-4=0
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Ecuación z^2+z+1=0
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Ecuación 8*x=2
- Expresar {x} en función de y en la ecuación:
- -17*x-15*y=-17
- 12*x-20*y=10
- -20*x-13*y=15
- 9*x+14*y=-10
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Expresiones idénticas
- (x- cinco)*(x^ dos + catorce *x- cuarenta y nueve)- trece *(x+ siete)= cero
- (x menos 5) multiplicar por (x al cuadrado más 14 multiplicar por x menos 49) menos 13 multiplicar por (x más 7) es igual a 0
- (x menos cinco) multiplicar por (x en el grado dos más cotangente de angente de orce multiplicar por x menos cuarenta y nueve) menos trece multiplicar por (x más siete) es igual a cero
- (x-5)*(x2+14*x-49)-13*(x+7)=0
- x-5*x2+14*x-49-13*x+7=0
- (x-5)*(x²+14*x-49)-13*(x+7)=0
- (x-5)*(x en el grado 2+14*x-49)-13*(x+7)=0
- (x-5)(x^2+14x-49)-13(x+7)=0
- (x-5)(x2+14x-49)-13(x+7)=0
- x-5x2+14x-49-13x+7=0
- x-5x^2+14x-49-13x+7=0
- (x-5)*(x^2+14*x-49)-13*(x+7)=O
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Expresiones semejantes
- (x-5)*(x^2+14*x+49)-13*(x+7)=0
- (x+5)*(x^2+14*x-49)-13*(x+7)=0
- (x-5)*(x^2+14*x-49)+13*(x+7)=0
- (x-5)*(x^2+14*x-49)-13*(x-7)=0
- (x-5)*(x^2-14*x-49)-13*(x+7)=0
(x-5)*(x^2+14*x-49)-13*(x+7)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \ (x - 5)*\x + 14*x - 49/ - 13*(x + 7) = 0
$$\left(x - 5\right) \left(\left(x^{2} + 14 x\right) - 49\right) - 13 \left(x + 7\right) = 0$$
Respuesta rápida
[src]
/ / / ______\\ / / ______\\\ / / ______\\ / / ______\\
| | |7*\/ 1177 || | |7*\/ 1177 ||| | |7*\/ 1177 || | |7*\/ 1177 ||
| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| ____ | \ 302 /| _____ | \ 302 /|| ____ | \ 302 /| _____ | \ 302 /|
| \/ 53 *sin|----------------| \/ 159 *cos|----------------|| \/ 53 *cos|----------------| \/ 159 *sin|----------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = -3 - 159*re|------------------------------------------| + I*|- 159*im|------------------------------------------| + ---------------------------- + -----------------------------| + ---------------------------- - -----------------------------
| _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2
|3 / ______ | 1 I*\/ 3 || | |3 / ______ | 1 I*\/ 3 || |
|\/ 8154 + 189*I*\/ 1177 *|- - - -------|| | |\/ 8154 + 189*I*\/ 1177 *|- - - -------|| |
\ \ 2 2 // \ \ \ 2 2 // /
$$x_{1} = -3 - \frac{\sqrt{159} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + \frac{\sqrt{53} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + i \left(- 159 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + \frac{\sqrt{53} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{159} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2}\right)$$
/ / / ______\\ / / ______\\\ / / ______\\ / / ______\\
| | |7*\/ 1177 || | |7*\/ 1177 ||| | |7*\/ 1177 || | |7*\/ 1177 ||
| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| ____ | \ 302 /| _____ | \ 302 /|| ____ | \ 302 /| _____ | \ 302 /|
| \/ 53 *sin|----------------| \/ 159 *cos|----------------|| \/ 53 *cos|----------------| \/ 159 *sin|----------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = -3 - 159*re|------------------------------------------| + I*|- 159*im|------------------------------------------| + ---------------------------- - -----------------------------| + ---------------------------- + -----------------------------
| _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2
|3 / ______ | 1 I*\/ 3 || | |3 / ______ | 1 I*\/ 3 || |
|\/ 8154 + 189*I*\/ 1177 *|- - + -------|| | |\/ 8154 + 189*I*\/ 1177 *|- - + -------|| |
\ \ 2 2 // \ \ \ 2 2 // /
$$x_{2} = -3 + \frac{\sqrt{159} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{53} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + i \left(- \frac{\sqrt{159} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{53} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)}\right)$$
_______________________
3 / ______
159 \/ 8154 + 189*I*\/ 1177
x3 = -3 - -------------------------- - --------------------------
_______________________ 3
3 / ______
\/ 8154 + 189*I*\/ 1177
$$x_{3} = -3 - \frac{\sqrt[3]{8154 + 189 \sqrt{1177} i}}{3} - \frac{159}{\sqrt[3]{8154 + 189 \sqrt{1177} i}}$$
x3 = -3 - (8154 + 189*sqrt(1177)*i)^(1/3)/3 - 159/(8154 + 189*sqrt(1177)*i)^(1/3)
Suma y producto de raíces
[src]
suma
/ / / ______\\ / / ______\\\ / / ______\\ / / ______\\ / / / ______\\ / / ______\\\ / / ______\\ / / ______\\
| | |7*\/ 1177 || | |7*\/ 1177 ||| | |7*\/ 1177 || | |7*\/ 1177 || | | |7*\/ 1177 || | |7*\/ 1177 ||| | |7*\/ 1177 || | |7*\/ 1177 ||
| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| ____ | \ 302 /| _____ | \ 302 /|| ____ | \ 302 /| _____ | \ 302 /| | ____ | \ 302 /| _____ | \ 302 /|| ____ | \ 302 /| _____ | \ 302 /| _______________________
| \/ 53 *sin|----------------| \/ 159 *cos|----------------|| \/ 53 *cos|----------------| \/ 159 *sin|----------------| | \/ 53 *sin|----------------| \/ 159 *cos|----------------|| \/ 53 *cos|----------------| \/ 159 *sin|----------------| 3 / ______
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / 159 \/ 8154 + 189*I*\/ 1177
-3 - 159*re|------------------------------------------| + I*|- 159*im|------------------------------------------| + ---------------------------- + -----------------------------| + ---------------------------- - ----------------------------- + -3 - 159*re|------------------------------------------| + I*|- 159*im|------------------------------------------| + ---------------------------- - -----------------------------| + ---------------------------- + ----------------------------- + -3 - -------------------------- - --------------------------
| _______________________ / ___\| | | _______________________ / ___\| 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 / ______
|\/ 8154 + 189*I*\/ 1177 *|- - - -------|| | |\/ 8154 + 189*I*\/ 1177 *|- - - -------|| | |\/ 8154 + 189*I*\/ 1177 *|- - + -------|| | |\/ 8154 + 189*I*\/ 1177 *|- - + -------|| | \/ 8154 + 189*I*\/ 1177
\ \ 2 2 // \ \ \ 2 2 // / \ \ 2 2 // \ \ \ 2 2 // /
$$\left(\left(-3 - \frac{\sqrt{159} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + \frac{\sqrt{53} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + i \left(- 159 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + \frac{\sqrt{53} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{159} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2}\right)\right) + \left(-3 + \frac{\sqrt{159} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{53} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + i \left(- \frac{\sqrt{159} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{53} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)}\right)\right)\right) + \left(-3 - \frac{\sqrt[3]{8154 + 189 \sqrt{1177} i}}{3} - \frac{159}{\sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)$$
=
/ / / ______\\ / / ______\\\ / / / ______\\ / / ______\\\
| | |7*\/ 1177 || | |7*\/ 1177 ||| | | |7*\/ 1177 || | |7*\/ 1177 |||
| |atan|----------|| |atan|----------||| | |atan|----------|| |atan|----------||| / / ______\\
_______________________ | ____ | \ 302 /| _____ | \ 302 /|| | ____ | \ 302 /| _____ | \ 302 /|| | |7*\/ 1177 ||
3 / ______ | \/ 53 *sin|----------------| \/ 159 *cos|----------------|| | \/ 53 *sin|----------------| \/ 159 *cos|----------------|| |atan|----------||
159 / 1 \ / 1 \ \/ 8154 + 189*I*\/ 1177 | / 1 \ \ 3 / \ 3 /| | / 1 \ \ 3 / \ 3 /| ____ | \ 302 /|
-9 - -------------------------- - 159*re|------------------------------------------| - 159*re|------------------------------------------| - -------------------------- + I*|- 159*im|------------------------------------------| + ---------------------------- - -----------------------------| + I*|- 159*im|------------------------------------------| + ---------------------------- + -----------------------------| + \/ 53 *cos|----------------|
_______________________ | _______________________ / ___\| | _______________________ / ___\| 3 | | _______________________ / ___\| 2 2 | | | _______________________ / ___\| 2 2 | \ 3 /
3 / ______ |3 / ______ | 1 I*\/ 3 || |3 / ______ | 1 I*\/ 3 || | |3 / ______ | 1 I*\/ 3 || | | |3 / ______ | 1 I*\/ 3 || |
\/ 8154 + 189*I*\/ 1177 |\/ 8154 + 189*I*\/ 1177 *|- - + -------|| |\/ 8154 + 189*I*\/ 1177 *|- - - -------|| | |\/ 8154 + 189*I*\/ 1177 *|- - + -------|| | | |\/ 8154 + 189*I*\/ 1177 *|- - - -------|| |
\ \ 2 2 // \ \ 2 2 // \ \ \ 2 2 // / \ \ \ 2 2 // /
$$-9 - 159 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} - 159 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + \sqrt{53} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)} - \frac{\sqrt[3]{8154 + 189 \sqrt{1177} i}}{3} + i \left(- \frac{\sqrt{159} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{53} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)}\right) + i \left(- 159 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + \frac{\sqrt{53} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{159} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2}\right) - \frac{159}{\sqrt[3]{8154 + 189 \sqrt{1177} i}}$$
producto
/ / / / ______\\ / / ______\\\ / / ______\\ / / ______\\\ / / / / ______\\ / / ______\\\ / / ______\\ / / ______\\\ | | | |7*\/ 1177 || | |7*\/ 1177 ||| | |7*\/ 1177 || | |7*\/ 1177 ||| | | | |7*\/ 1177 || | |7*\/ 1177 ||| | |7*\/ 1177 || | |7*\/ 1177 ||| | | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | | ____ | \ 302 /| _____ | \ 302 /|| ____ | \ 302 /| _____ | \ 302 /|| | | ____ | \ 302 /| _____ | \ 302 /|| ____ | \ 302 /| _____ | \ 302 /|| / _______________________\ | | \/ 53 *sin|----------------| \/ 159 *cos|----------------|| \/ 53 *cos|----------------| \/ 159 *sin|----------------|| | | \/ 53 *sin|----------------| \/ 159 *cos|----------------|| \/ 53 *cos|----------------| \/ 159 *sin|----------------|| | 3 / ______ | | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | 159 \/ 8154 + 189*I*\/ 1177 | |-3 - 159*re|------------------------------------------| + I*|- 159*im|------------------------------------------| + ---------------------------- + -----------------------------| + ---------------------------- - -----------------------------|*|-3 - 159*re|------------------------------------------| + I*|- 159*im|------------------------------------------| + ---------------------------- - -----------------------------| + ---------------------------- + -----------------------------|*|-3 - -------------------------- - --------------------------| | | _______________________ / ___\| | | _______________________ / ___\| 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 / ______ | | |\/ 8154 + 189*I*\/ 1177 *|- - - -------|| | |\/ 8154 + 189*I*\/ 1177 *|- - - -------|| | | | |\/ 8154 + 189*I*\/ 1177 *|- - + -------|| | |\/ 8154 + 189*I*\/ 1177 *|- - + -------|| | | \ \/ 8154 + 189*I*\/ 1177 / \ \ \ 2 2 // \ \ \ 2 2 // / / \ \ \ 2 2 // \ \ \ 2 2 // / /
$$\left(-3 - \frac{\sqrt{159} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + \frac{\sqrt{53} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + i \left(- 159 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + \frac{\sqrt{53} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{159} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2}\right)\right) \left(-3 + \frac{\sqrt{159} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{53} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)} + i \left(- \frac{\sqrt{159} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} + \frac{\sqrt{53} \sin{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)}}{2} - 159 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)}\right)\right) \left(-3 - \frac{\sqrt[3]{8154 + 189 \sqrt{1177} i}}{3} - \frac{159}{\sqrt[3]{8154 + 189 \sqrt{1177} i}}\right)$$
=
/ / / ______\\ / / ______\\\
| | |7*\/ 1177 || | |7*\/ 1177 |||
/ ____________________ / ____________________\\ | |2*atan|----------|| |atan|----------|||
| 3 / ______ | 3 / ______ || | | \ 302 /| ____ | \ 302 /||
\53 + \/ 302 + 7*I*\/ 1177 *\3 + \/ 302 + 7*I*\/ 1177 //*|44 - 106*cos|------------------| + 6*\/ 53 *cos|----------------||
\ \ 3 / \ 3 //
--------------------------------------------------------------------------------------------------------------------------------
____________________
3 / ______
\/ 302 + 7*I*\/ 1177
$$\frac{\left(53 + \left(3 + \sqrt[3]{302 + 7 \sqrt{1177} i}\right) \sqrt[3]{302 + 7 \sqrt{1177} i}\right) \left(- 106 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)} + 6 \sqrt{53} \cos{\left(\frac{\operatorname{atan}{\left(\frac{7 \sqrt{1177}}{302} \right)}}{3} \right)} + 44\right)}{\sqrt[3]{302 + 7 \sqrt{1177} i}}$$
(53 + (302 + 7*i*sqrt(1177))^(1/3)*(3 + (302 + 7*i*sqrt(1177))^(1/3)))*(44 - 106*cos(2*atan(7*sqrt(1177)/302)/3) + 6*sqrt(53)*cos(atan(7*sqrt(1177)/302)/3))/(302 + 7*i*sqrt(1177))^(1/3)
Respuesta numérica
[src]
x1 = 6.89852577542074
x2 = 1.29813623880074
x3 = -17.1966620142215
x3 = -17.1966620142215