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- La ecuación:
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
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Ecuación x^2+4=5x
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Ecuación x(x^2+2x+1)=6(x+1)
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Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
-
Expresiones idénticas
- iz(z^ dos + siete)+ seis = cero
- iz(z al cuadrado más 7) más 6 es igual a 0
- iz(z en el grado dos más siete) más seis es igual a cero
- iz(z2+7)+6=0
- izz2+7+6=0
- iz(z²+7)+6=0
- iz(z en el grado 2+7)+6=0
- izz^2+7+6=0
- iz(z^2+7)+6=O
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Expresiones semejantes
- iz(z^2-7)+6=0
- iz(z^2+7)-6=0
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Expresiones con funciones
- iz
- iz^2+(3-2i)*z-6=0
- iz^2+(3-2i)z+(-6)=0
- iz=1
- iz^2-(4+i)z+6+12i=0
iz(z^2+7)+6=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
Suma y producto de raíces
[src]
suma
/ / / ___\\ / / ___\\\ / / ___\\ / / ___\\ / / / ___\\ / / ___\\\ / / ___\\ / / ___\\ / / ___\\
| | |9*\/ 3 || | |9*\/ 3 ||| | |9*\/ 3 || | |9*\/ 3 || | | |9*\/ 3 || | |9*\/ 3 ||| | |9*\/ 3 || | |9*\/ 3 || | |9*\/ 3 ||
| |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------|| | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------|| |atan|-------||
| ___ | \ 10 /| ____ | \ 10 /|| ___ | \ 10 /| ____ | \ 10 /| | ___ | \ 10 /| ____ | \ 10 /|| ___ | \ 10 /| ____ | \ 10 /| ____ | \ 10 /|
| \/ 7 *cos|-------------| \/ 21 *sin|-------------|| \/ 7 *sin|-------------| \/ 21 *cos|-------------| | \/ 7 *cos|-------------| \/ 21 *sin|-------------|| \/ 7 *sin|-------------| \/ 21 *cos|-------------| 2*I*\/ 21 *sin|-------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / \ 3 /
7*re|-------------------------------------| + I*|7*im|-------------------------------------| + ------------------------ - -------------------------| + ------------------------ + ------------------------- + 7*re|-------------------------------------| + I*|7*im|-------------------------------------| - ------------------------ - -------------------------| - ------------------------ + ------------------------- + -----------------------------
|/ ___\ __________________| | |/ ___\ __________________| 2 6 | 2 6 |/ ___\ __________________| | |/ ___\ __________________| 2 6 | 2 6 3
|| 1 I*\/ 3 | 3 / ___ | | || 1 I*\/ 3 | 3 / ___ | | || 1 I*\/ 3 | 3 / ___ | | || 1 I*\/ 3 | 3 / ___ | |
||- - - -------|*\/ -81*I + 30*\/ 3 | | ||- - - -------|*\/ -81*I + 30*\/ 3 | | ||- - + -------|*\/ -81*I + 30*\/ 3 | | ||- - + -------|*\/ -81*I + 30*\/ 3 | |
\\ 2 2 / / \ \\ 2 2 / / / \\ 2 2 / / \ \\ 2 2 / / /
$$\left(\left(- \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} - \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} - \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6}\right)\right) + \left(7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(- \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + 7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2}\right)\right)\right) + \frac{2 \sqrt{21} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3}$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ / / ___\\ / / ___\\
| | |9*\/ 3 || | |9*\/ 3 ||| | | |9*\/ 3 || | |9*\/ 3 ||| | |9*\/ 3 || | |9*\/ 3 ||
| |atan|-------|| |atan|-------||| | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||
| ___ | \ 10 /| ____ | \ 10 /|| | ___ | \ 10 /| ____ | \ 10 /|| ____ | \ 10 /| ____ | \ 10 /|
| \/ 7 *cos|-------------| \/ 21 *sin|-------------|| | \/ 7 *cos|-------------| \/ 21 *sin|-------------|| \/ 21 *cos|-------------| 2*I*\/ 21 *sin|-------------|
/ 1 \ / 1 \ | / 1 \ \ 3 / \ 3 /| | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
7*re|-------------------------------------| + 7*re|-------------------------------------| + I*|7*im|-------------------------------------| - ------------------------ - -------------------------| + I*|7*im|-------------------------------------| + ------------------------ - -------------------------| + ------------------------- + -----------------------------
|/ ___\ __________________| |/ ___\ __________________| | |/ ___\ __________________| 2 6 | | |/ ___\ __________________| 2 6 | 3 3
|| 1 I*\/ 3 | 3 / ___ | || 1 I*\/ 3 | 3 / ___ | | || 1 I*\/ 3 | 3 / ___ | | | || 1 I*\/ 3 | 3 / ___ | |
||- - + -------|*\/ -81*I + 30*\/ 3 | ||- - - -------|*\/ -81*I + 30*\/ 3 | | ||- - + -------|*\/ -81*I + 30*\/ 3 | | | ||- - - -------|*\/ -81*I + 30*\/ 3 | |
\\ 2 2 / / \\ 2 2 / / \ \\ 2 2 / / / \ \\ 2 2 / / /
$$7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3} + i \left(7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} - \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} - \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6}\right) + \frac{2 \sqrt{21} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3} + i \left(- \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + 7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2}\right)$$
producto
/ / / / ___\\ / / ___\\\ / / ___\\ / / ___\\\ / / / / ___\\ / / ___\\\ / / ___\\ / / ___\\\ / / ___\\ | | | |9*\/ 3 || | |9*\/ 3 ||| | |9*\/ 3 || | |9*\/ 3 ||| | | | |9*\/ 3 || | |9*\/ 3 ||| | |9*\/ 3 || | |9*\/ 3 ||| | |9*\/ 3 || | | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||| | | |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||| |atan|-------|| | | ___ | \ 10 /| ____ | \ 10 /|| ___ | \ 10 /| ____ | \ 10 /|| | | ___ | \ 10 /| ____ | \ 10 /|| ___ | \ 10 /| ____ | \ 10 /|| ____ | \ 10 /| | | \/ 7 *cos|-------------| \/ 21 *sin|-------------|| \/ 7 *sin|-------------| \/ 21 *cos|-------------|| | | \/ 7 *cos|-------------| \/ 21 *sin|-------------|| \/ 7 *sin|-------------| \/ 21 *cos|-------------|| 2*I*\/ 21 *sin|-------------| | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| \ 3 / |7*re|-------------------------------------| + I*|7*im|-------------------------------------| + ------------------------ - -------------------------| + ------------------------ + -------------------------|*|7*re|-------------------------------------| + I*|7*im|-------------------------------------| - ------------------------ - -------------------------| - ------------------------ + -------------------------|*----------------------------- | |/ ___\ __________________| | |/ ___\ __________________| 2 6 | 2 6 | | |/ ___\ __________________| | |/ ___\ __________________| 2 6 | 2 6 | 3 | || 1 I*\/ 3 | 3 / ___ | | || 1 I*\/ 3 | 3 / ___ | | | | || 1 I*\/ 3 | 3 / ___ | | || 1 I*\/ 3 | 3 / ___ | | | | ||- - - -------|*\/ -81*I + 30*\/ 3 | | ||- - - -------|*\/ -81*I + 30*\/ 3 | | | | ||- - + -------|*\/ -81*I + 30*\/ 3 | | ||- - + -------|*\/ -81*I + 30*\/ 3 | | | \ \\ 2 2 / / \ \\ 2 2 / / / / \ \\ 2 2 / / \ \\ 2 2 / / / /
$$\left(- \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} - \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} - \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6}\right)\right) \left(7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(- \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + 7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2}\right)\right) \frac{2 \sqrt{21} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3}$$
=
6*I
$$6 i$$
6*i
Respuesta rápida
[src]
/ / / ___\\ / / ___\\\ / / ___\\ / / ___\\
| | |9*\/ 3 || | |9*\/ 3 ||| | |9*\/ 3 || | |9*\/ 3 ||
| |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||
| ___ | \ 10 /| ____ | \ 10 /|| ___ | \ 10 /| ____ | \ 10 /|
| \/ 7 *cos|-------------| \/ 21 *sin|-------------|| \/ 7 *sin|-------------| \/ 21 *cos|-------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
z1 = 7*re|-------------------------------------| + I*|7*im|-------------------------------------| + ------------------------ - -------------------------| + ------------------------ + -------------------------
|/ ___\ __________________| | |/ ___\ __________________| 2 6 | 2 6
|| 1 I*\/ 3 | 3 / ___ | | || 1 I*\/ 3 | 3 / ___ | |
||- - - -------|*\/ -81*I + 30*\/ 3 | | ||- - - -------|*\/ -81*I + 30*\/ 3 | |
\\ 2 2 / / \ \\ 2 2 / / /
$$z_{1} = 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(- \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + 7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2}\right)$$
/ / / ___\\ / / ___\\\ / / ___\\ / / ___\\
| | |9*\/ 3 || | |9*\/ 3 ||| | |9*\/ 3 || | |9*\/ 3 ||
| |atan|-------|| |atan|-------||| |atan|-------|| |atan|-------||
| ___ | \ 10 /| ____ | \ 10 /|| ___ | \ 10 /| ____ | \ 10 /|
| \/ 7 *cos|-------------| \/ 21 *sin|-------------|| \/ 7 *sin|-------------| \/ 21 *cos|-------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
z2 = 7*re|-------------------------------------| + I*|7*im|-------------------------------------| - ------------------------ - -------------------------| - ------------------------ + -------------------------
|/ ___\ __________________| | |/ ___\ __________________| 2 6 | 2 6
|| 1 I*\/ 3 | 3 / ___ | | || 1 I*\/ 3 | 3 / ___ | |
||- - + -------|*\/ -81*I + 30*\/ 3 | | ||- - + -------|*\/ -81*I + 30*\/ 3 | |
\\ 2 2 / / \ \\ 2 2 / / /
$$z_{2} = - \frac{\sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} + 7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} + \frac{\sqrt{21} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6} + i \left(7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{30 \sqrt{3} - 81 i}}\right)} - \frac{\sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{2} - \frac{\sqrt{21} \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{6}\right)$$
/ / ___\\
| |9*\/ 3 ||
|atan|-------||
____ | \ 10 /|
2*I*\/ 21 *sin|-------------|
\ 3 /
z3 = -----------------------------
3
$$z_{3} = \frac{2 \sqrt{21} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{9 \sqrt{3}}{10} \right)}}{3} \right)}}{3}$$
z3 = 2*sqrt(21)*i*sin(atan(9*sqrt(3)/10)/3)/3
Respuesta numérica
[src]
z1 = -5.29395592033938e-23 - 3.0*i
z2 = 1.35525271560688e-20 + 2.0*i
z3 = 2.11758236813575e-22 + 1.0*i
z3 = 2.11758236813575e-22 + 1.0*i