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Expresiones idénticas
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- x multiplicar por (x en el grado dos menos uno) menos uno multiplicar por tres dividir por veinte es igual a cero
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- x*x2-1-1*3/20=0
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- x(x^2-1)-13/20=0
- x(x2-1)-13/20=0
- xx2-1-13/20=0
- xx^2-1-13/20=0
- x*(x^2-1)-1*3/20=O
- x*(x^2-1)-1*3 dividir por 20=0
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Expresiones semejantes
- x*(x^2-1)+1*3/20=0
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x*(x^2-1)-1*3/20=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
/ / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\
| |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||
|atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||
| \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|
sin|--------------| ||- - - -------|*3 / -- + ---------- | | cos|--------------| ||- - - -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|
\ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /
x1 = ------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------
2 3 \ 2 3 6 / 6
$$x_{1} = - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(- \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3}\right)$$
/ 1 \ / / 1 \ \
/ / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\
| |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||
|atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||
| \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|
sin|--------------| ||- - + -------|*3 / -- + ---------- | |cos|--------------| ||- - + -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|
\ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /
x2 = - ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - -------------------------
2 3 \ 2 3 6 / 6
$$x_{2} = \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} - \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2}\right)$$
_________________
/ ______
/ 3 I*\/ 4071 1
x3 = 3 / -- + ---------- + ------------------------
\/ 40 360 _________________
/ ______
/ 3 I*\/ 4071
3*3 / -- + ----------
\/ 40 360
$$x_{3} = \frac{1}{3 \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}} + \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}$$
x3 = 1/(3*(3/40 + sqrt(4071)*i/360)^(1/3)) + (3/40 + sqrt(4071)*i/360)^(1/3)
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
/ / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\ / / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\
| |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 || | |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||
|atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------|| |atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||
| \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /| | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /| _________________
sin|--------------| ||- - - -------|*3 / -- + ---------- | | cos|--------------| ||- - - -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------| sin|--------------| ||- - + -------|*3 / -- + ---------- | |cos|--------------| ||- - + -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------| / ______
\ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 / \ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 / / 3 I*\/ 4071 1
------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - ------------------------- + - ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - ------------------------- + 3 / -- + ---------- + ------------------------
2 3 \ 2 3 6 / 6 2 3 \ 2 3 6 / 6 \/ 40 360 _________________
/ ______
/ 3 I*\/ 4071
3*3 / -- + ----------
\/ 40 360
$$\left(\frac{1}{3 \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}} + \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}\right) + \left(\left(\frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} - \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2}\right)\right) + \left(- \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(- \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
re|--------------------------------------| re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\
| _________________| | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||
|/ ___\ / ______ | |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||
_________________ || 1 I*\/ 3 | / 3 I*\/ 4071 | || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|
/ ______ ||- - + -------|*3 / -- + ---------- | ||- - - -------|*3 / -- + ---------- | |cos|--------------| ||- - + -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| | cos|--------------| ||- - - -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|
/ 3 I*\/ 4071 1 \\ 2 2 / \/ 40 360 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /
3 / -- + ---------- + ------------------------ + ------------------------------------------ + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------
\/ 40 360 _________________ 3 3 \ 2 3 6 / \ 2 3 6 / 3
/ ______
/ 3 I*\/ 4071
3*3 / -- + ----------
\/ 40 360
$$- \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{3} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{1}{3 \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}} + i \left(- \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3}\right) + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2}\right) + \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| / / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\| | / / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\|
| | |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||| | | |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 |||
| |atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||| | |atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------|||
| | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|| | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|| / _________________ \
|sin|--------------| ||- - - -------|*3 / -- + ---------- | | cos|--------------| ||- - - -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|| | sin|--------------| ||- - + -------|*3 / -- + ---------- | |cos|--------------| ||- - + -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|| | / ______ |
| \ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /| | \ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /| | / 3 I*\/ 4071 1 |
|------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------|*|- ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - -------------------------|*|3 / -- + ---------- + ------------------------|
\ 2 3 \ 2 3 6 / 6 / \ 2 3 \ 2 3 6 / 6 / |\/ 40 360 _________________|
| / ______ |
| / 3 I*\/ 4071 |
| 3*3 / -- + ---------- |
\ \/ 40 360 /
$$\left(- \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(- \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3}\right)\right) \left(\frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} - \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2}\right)\right) \left(\frac{1}{3 \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}} + \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}\right)$$
=
/ / / ______\\\
| | |\/ 4071 |||
| |2*atan|--------||| / 2/3\
| | \ 27 /|| | 3 ____ 3 ____ / ______\ |
|-12 + 24*cos|----------------||*\20*\/ 45 + \/ 75 *\27 + I*\/ 4071 / /
\ \ 3 //
--------------------------------------------------------------------------
_________________
3 / ______
1080*\/ 27 + I*\/ 4071
$$\frac{\left(-12 + 24 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}\right) \left(20 \sqrt[3]{45} + \sqrt[3]{75} \left(27 + \sqrt{4071} i\right)^{\frac{2}{3}}\right)}{1080 \sqrt[3]{27 + \sqrt{4071} i}}$$
(-12 + 24*cos(2*atan(sqrt(4071)/27)/3))*(20*45^(1/3) + 75^(1/3)*(27 + i*sqrt(4071))^(2/3))/(1080*(27 + i*sqrt(4071))^(1/3))
Respuesta numérica
[src]
x1 = -0.153625697823484
x2 = 1.0679230136897
x3 = -0.914297315866213
x3 = -0.914297315866213