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- La ecuación:
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Ecuación 8*x=2
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Ecuación 3^x=81
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Ecuación x^2=12
-
Ecuación -27x+220=-5x
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -17*x+2*y=9
-
Expresiones idénticas
- (x- cuatro)(x²+16x+ sesenta y cuatro)= trece (x- ocho)
- (x menos 4)(x² más 16x más 64) es igual a 13(x menos 8)
- (x menos cuatro)(x² más 16x más sesenta y cuatro) es igual a trece (x menos ocho)
- x-4x²+16x+64=13x-8
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Expresiones semejantes
- (x+4)(x²+16x+64)=13(x-8)
- (x-4)(x²+16x-64)=13(x-8)
- 13*x-8*x=(11/2)
- x^2+(5*10^-13*x)-8*10^-9=0
- (x-4)(x²+16x+64)=13(x+8)
- (x-4)(x²-16x+64)=13(x-8)
- (x+1)(3x-8)=x^-5
- sqrt(12*x+3)=sqrt(4*x^2+13*x-8)
(x-4)(x²+16x+64)=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 + 64/ = 13*(x - 8)
$$\left(x - 4\right) \left(\left(x^{2} + 16 x\right) + 64\right) = 13 \left(x - 8\right)$$
Suma y producto de raíces
[src]
suma
/ / / ________\\ / / ________\\\ / / ________\\ / / ________\\ / / / ________\\ / / ________\\\ / / ________\\ / / ________\\
| | |\/ 665067 || | |\/ 665067 ||| | |\/ 665067 || | |\/ 665067 || | | |\/ 665067 || | |\/ 665067 ||| | |\/ 665067 || | |\/ 665067 ||
| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| ____ | \ 126 /| _____ | \ 126 /|| ____ | \ 126 /| _____ | \ 126 /| | ____ | \ 126 /| _____ | \ 126 /|| ____ | \ 126 /| _____ | \ 126 /| ______________________
| \/ 61 *cos|----------------| \/ 183 *sin|----------------|| \/ 61 *sin|----------------| \/ 183 *cos|----------------| | \/ 61 *cos|----------------| \/ 183 *sin|----------------|| \/ 61 *sin|----------------| \/ 183 *cos|----------------| 3 / ________
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / 61 \/ 378 + 3*I*\/ 665067
-4 - 61*re|-----------------------------------------| + I*|- 61*im|-----------------------------------------| + ---------------------------- + -----------------------------| - ---------------------------- + ----------------------------- + -4 - 61*re|-----------------------------------------| + I*|- 61*im|-----------------------------------------| - ---------------------------- + -----------------------------| + ---------------------------- + ----------------------------- + -4 - ------------------------- - -------------------------
| ______________________ / ___\| | | ______________________ / ___\| 2 6 | 2 6 | ______________________ / ___\| | | ______________________ / ___\| 2 6 | 2 6 ______________________ 3
|3 / ________ | 1 I*\/ 3 || | |3 / ________ | 1 I*\/ 3 || | |3 / ________ | 1 I*\/ 3 || | |3 / ________ | 1 I*\/ 3 || | 3 / ________
|\/ 378 + 3*I*\/ 665067 *|- - - -------|| | |\/ 378 + 3*I*\/ 665067 *|- - - -------|| | |\/ 378 + 3*I*\/ 665067 *|- - + -------|| | |\/ 378 + 3*I*\/ 665067 *|- - + -------|| | \/ 378 + 3*I*\/ 665067
\ \ 2 2 // \ \ \ 2 2 // / \ \ 2 2 // \ \ \ 2 2 // /
$$\left(\left(-4 + \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} - 61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + i \left(- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} - 61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)}\right)\right) + \left(-4 - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} - 61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} + i \left(- 61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} + \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2}\right)\right)\right) + \left(-4 - \frac{\sqrt[3]{378 + 3 \sqrt{665067} i}}{3} - \frac{61}{\sqrt[3]{378 + 3 \sqrt{665067} i}}\right)$$
=
/ / / ________\\ / / ________\\\ / / / ________\\ / / ________\\\ / / ________\\
| | |\/ 665067 || | |\/ 665067 ||| | | |\/ 665067 || | |\/ 665067 ||| | |\/ 665067 ||
| |atan|----------|| |atan|----------||| | |atan|----------|| |atan|----------||| |atan|----------||
______________________ | ____ | \ 126 /| _____ | \ 126 /|| | ____ | \ 126 /| _____ | \ 126 /|| _____ | \ 126 /|
3 / ________ | \/ 61 *cos|----------------| \/ 183 *sin|----------------|| | \/ 61 *cos|----------------| \/ 183 *sin|----------------|| \/ 183 *cos|----------------|
61 / 1 \ / 1 \ \/ 378 + 3*I*\/ 665067 | / 1 \ \ 3 / \ 3 /| | / 1 \ \ 3 / \ 3 /| \ 3 /
-12 - ------------------------- - 61*re|-----------------------------------------| - 61*re|-----------------------------------------| - ------------------------- + I*|- 61*im|-----------------------------------------| - ---------------------------- + -----------------------------| + I*|- 61*im|-----------------------------------------| + ---------------------------- + -----------------------------| + -----------------------------
______________________ | ______________________ / ___\| | ______________________ / ___\| 3 | | ______________________ / ___\| 2 6 | | | ______________________ / ___\| 2 6 | 3
3 / ________ |3 / ________ | 1 I*\/ 3 || |3 / ________ | 1 I*\/ 3 || | |3 / ________ | 1 I*\/ 3 || | | |3 / ________ | 1 I*\/ 3 || |
\/ 378 + 3*I*\/ 665067 |\/ 378 + 3*I*\/ 665067 *|- - + -------|| |\/ 378 + 3*I*\/ 665067 *|- - - -------|| | |\/ 378 + 3*I*\/ 665067 *|- - + -------|| | | |\/ 378 + 3*I*\/ 665067 *|- - - -------|| |
\ \ 2 2 // \ \ 2 2 // \ \ \ 2 2 // / \ \ \ 2 2 // /
$$-12 - 61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} - 61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{3} - \frac{\sqrt[3]{378 + 3 \sqrt{665067} i}}{3} + i \left(- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} - 61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)}\right) + i \left(- 61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} + \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2}\right) - \frac{61}{\sqrt[3]{378 + 3 \sqrt{665067} i}}$$
producto
/ / / / ________\\ / / ________\\\ / / ________\\ / / ________\\\ / / / / ________\\ / / ________\\\ / / ________\\ / / ________\\\ | | | |\/ 665067 || | |\/ 665067 ||| | |\/ 665067 || | |\/ 665067 ||| | | | |\/ 665067 || | |\/ 665067 ||| | |\/ 665067 || | |\/ 665067 ||| | | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | | ____ | \ 126 /| _____ | \ 126 /|| ____ | \ 126 /| _____ | \ 126 /|| | | ____ | \ 126 /| _____ | \ 126 /|| ____ | \ 126 /| _____ | \ 126 /|| / ______________________\ | | \/ 61 *cos|----------------| \/ 183 *sin|----------------|| \/ 61 *sin|----------------| \/ 183 *cos|----------------|| | | \/ 61 *cos|----------------| \/ 183 *sin|----------------|| \/ 61 *sin|----------------| \/ 183 *cos|----------------|| | 3 / ________ | | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | 61 \/ 378 + 3*I*\/ 665067 | |-4 - 61*re|-----------------------------------------| + I*|- 61*im|-----------------------------------------| + ---------------------------- + -----------------------------| - ---------------------------- + -----------------------------|*|-4 - 61*re|-----------------------------------------| + I*|- 61*im|-----------------------------------------| - ---------------------------- + -----------------------------| + ---------------------------- + -----------------------------|*|-4 - ------------------------- - -------------------------| | | ______________________ / ___\| | | ______________________ / ___\| 2 6 | 2 6 | | | ______________________ / ___\| | | ______________________ / ___\| 2 6 | 2 6 | | ______________________ 3 | | |3 / ________ | 1 I*\/ 3 || | |3 / ________ | 1 I*\/ 3 || | | | |3 / ________ | 1 I*\/ 3 || | |3 / ________ | 1 I*\/ 3 || | | | 3 / ________ | | |\/ 378 + 3*I*\/ 665067 *|- - - -------|| | |\/ 378 + 3*I*\/ 665067 *|- - - -------|| | | | |\/ 378 + 3*I*\/ 665067 *|- - + -------|| | |\/ 378 + 3*I*\/ 665067 *|- - + -------|| | | \ \/ 378 + 3*I*\/ 665067 / \ \ \ 2 2 // \ \ \ 2 2 // / / \ \ \ 2 2 // \ \ \ 2 2 // / /
$$\left(-4 - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} - 61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} + i \left(- 61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} + \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2}\right)\right) \left(-4 + \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} - 61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + i \left(- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} - 61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)}\right)\right) \left(-4 - \frac{\sqrt[3]{378 + 3 \sqrt{665067} i}}{3} - \frac{61}{\sqrt[3]{378 + 3 \sqrt{665067} i}}\right)$$
=
/ / / ________\\ / / ________\\\
| | |\/ 665067 || | |\/ 665067 |||
/ ______________________ / ______________________\\ | |2*atan|----------|| |atan|----------|||
2/3 | 3 / ________ | 3 / ________ || | | \ 126 /| _____ | \ 126 /||
3 *\183 + \/ 378 + 3*I*\/ 665067 *\12 + \/ 378 + 3*I*\/ 665067 //*|156 - 1464*cos|------------------| + 96*\/ 183 *cos|----------------||
\ \ 3 / \ 3 //
-----------------------------------------------------------------------------------------------------------------------------------------------
____________________
3 / ________
324*\/ 126 + I*\/ 665067
$$\frac{3^{\frac{2}{3}} \left(183 + \left(12 + \sqrt[3]{378 + 3 \sqrt{665067} i}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}\right) \left(- 1464 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)} + 156 + 96 \sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}\right)}{324 \sqrt[3]{126 + \sqrt{665067} i}}$$
3^(2/3)*(183 + (378 + 3*i*sqrt(665067))^(1/3)*(12 + (378 + 3*i*sqrt(665067))^(1/3)))*(156 - 1464*cos(2*atan(sqrt(665067)/126)/3) + 96*sqrt(183)*cos(atan(sqrt(665067)/126)/3))/(324*(126 + i*sqrt(665067))^(1/3))
Respuesta rápida
[src]
/ / / ________\\ / / ________\\\ / / ________\\ / / ________\\
| | |\/ 665067 || | |\/ 665067 ||| | |\/ 665067 || | |\/ 665067 ||
| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| ____ | \ 126 /| _____ | \ 126 /|| ____ | \ 126 /| _____ | \ 126 /|
| \/ 61 *cos|----------------| \/ 183 *sin|----------------|| \/ 61 *sin|----------------| \/ 183 *cos|----------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = -4 - 61*re|-----------------------------------------| + I*|- 61*im|-----------------------------------------| + ---------------------------- + -----------------------------| - ---------------------------- + -----------------------------
| ______________________ / ___\| | | ______________________ / ___\| 2 6 | 2 6
|3 / ________ | 1 I*\/ 3 || | |3 / ________ | 1 I*\/ 3 || |
|\/ 378 + 3*I*\/ 665067 *|- - - -------|| | |\/ 378 + 3*I*\/ 665067 *|- - - -------|| |
\ \ 2 2 // \ \ \ 2 2 // /
$$x_{1} = -4 - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} - 61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} + i \left(- 61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} + \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2}\right)$$
/ / / ________\\ / / ________\\\ / / ________\\ / / ________\\
| | |\/ 665067 || | |\/ 665067 ||| | |\/ 665067 || | |\/ 665067 ||
| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| ____ | \ 126 /| _____ | \ 126 /|| ____ | \ 126 /| _____ | \ 126 /|
| \/ 61 *cos|----------------| \/ 183 *sin|----------------|| \/ 61 *sin|----------------| \/ 183 *cos|----------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = -4 - 61*re|-----------------------------------------| + I*|- 61*im|-----------------------------------------| - ---------------------------- + -----------------------------| + ---------------------------- + -----------------------------
| ______________________ / ___\| | | ______________________ / ___\| 2 6 | 2 6
|3 / ________ | 1 I*\/ 3 || | |3 / ________ | 1 I*\/ 3 || |
|\/ 378 + 3*I*\/ 665067 *|- - + -------|| | |\/ 378 + 3*I*\/ 665067 *|- - + -------|| |
\ \ 2 2 // \ \ \ 2 2 // /
$$x_{2} = -4 + \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} - 61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)} + i \left(- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{2} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{665067}}{126} \right)}}{3} \right)}}{6} - 61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{378 + 3 \sqrt{665067} i}}\right)}\right)$$
______________________
3 / ________
61 \/ 378 + 3*I*\/ 665067
x3 = -4 - ------------------------- - -------------------------
______________________ 3
3 / ________
\/ 378 + 3*I*\/ 665067
$$x_{3} = -4 - \frac{\sqrt[3]{378 + 3 \sqrt{665067} i}}{3} - \frac{61}{\sqrt[3]{378 + 3 \sqrt{665067} i}}$$
x3 = -4 - (378 + 3*sqrt(665067)*i)^(1/3)/3 - 61/(378 + 3*sqrt(665067)*i)^(1/3)
Respuesta numérica
[src]
x1 = -3.53938148919968
x2 = 3.56974670213188
x3 = -12.0303652129322
x3 = -12.0303652129322