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Expresiones semejantes
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- 36/4-x^2-2=1-x/x+2-9/x-2
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36/4-x^2+2=1-x/x+2-9/x-2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 x 9
9 - x + 2 = 1 - - + 2 - - - 2
x x
$$\left(9 - x^{2}\right) + 2 = \left(\left(\left(1 - \frac{x}{x}\right) + 2\right) - \frac{9}{x}\right) - 2$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
11*re|-------------------------------------| |11*im|-------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ________________| | | ________________| | |\/ 9411 || | |\/ 9411 ||| | |\/ 9411 || | |\/ 9411 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|--------|| |atan|--------||| |atan|--------|| |atan|--------||
|| 1 I*\/ 3 | / 9 I*\/ 9411 | | || 1 I*\/ 3 | / 9 I*\/ 9411 | ____ | \ 81 /| ____ | \ 81 /|| ____ | \ 81 /| ____ | \ 81 /|
||- - - -------|*3 / - + ---------- | | ||- - - -------|*3 / - + ---------- | \/ 11 *cos|--------------| \/ 33 *sin|--------------|| \/ 11 *sin|--------------| \/ 33 *cos|--------------|
\\ 2 2 / \/ 2 18 / | \\ 2 2 / \/ 2 18 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = -------------------------------------------- + I*|-------------------------------------------- - -------------------------- - --------------------------| + -------------------------- - --------------------------
3 \ 3 2 6 / 2 6
$$x_{1} = - \frac{\sqrt{33} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{11 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} + \frac{\sqrt{11} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{11} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} - \frac{\sqrt{33} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{11 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3}\right)$$
/ 1 \ / / 1 \ \
11*re|-------------------------------------| |11*im|-------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ________________| | | ________________| | |\/ 9411 || | |\/ 9411 ||| | |\/ 9411 || | |\/ 9411 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|--------|| |atan|--------||| |atan|--------|| |atan|--------||
|| 1 I*\/ 3 | / 9 I*\/ 9411 | | || 1 I*\/ 3 | / 9 I*\/ 9411 | ____ | \ 81 /| ____ | \ 81 /|| ____ | \ 81 /| ____ | \ 81 /|
||- - + -------|*3 / - + ---------- | | ||- - + -------|*3 / - + ---------- | \/ 11 *cos|--------------| \/ 33 *sin|--------------|| \/ 11 *sin|--------------| \/ 33 *cos|--------------|
\\ 2 2 / \/ 2 18 / | \\ 2 2 / \/ 2 18 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = -------------------------------------------- + I*|-------------------------------------------- + -------------------------- - --------------------------| - -------------------------- - --------------------------
3 \ 3 2 6 / 2 6
$$x_{2} = \frac{11 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} - \frac{\sqrt{33} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} - \frac{\sqrt{11} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} + i \left(\frac{11 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} - \frac{\sqrt{33} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{\sqrt{11} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2}\right)$$
________________
/ ______
/ 9 I*\/ 9411 11
x3 = 3 / - + ---------- + -----------------------
\/ 2 18 ________________
/ ______
/ 9 I*\/ 9411
3*3 / - + ----------
\/ 2 18
$$x_{3} = \frac{11}{3 \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}} + \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}$$
x3 = 11/(3*(9/2 + sqrt(9411)*i/18)^(1/3)) + (9/2 + sqrt(9411)*i/18)^(1/3)
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
11*re|-------------------------------------| |11*im|-------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ 11*re|-------------------------------------| |11*im|-------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ________________| | | ________________| | |\/ 9411 || | |\/ 9411 ||| | |\/ 9411 || | |\/ 9411 || | ________________| | | ________________| | |\/ 9411 || | |\/ 9411 ||| | |\/ 9411 || | |\/ 9411 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|--------|| |atan|--------||| |atan|--------|| |atan|--------|| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|--------|| |atan|--------||| |atan|--------|| |atan|--------||
|| 1 I*\/ 3 | / 9 I*\/ 9411 | | || 1 I*\/ 3 | / 9 I*\/ 9411 | ____ | \ 81 /| ____ | \ 81 /|| ____ | \ 81 /| ____ | \ 81 /| || 1 I*\/ 3 | / 9 I*\/ 9411 | | || 1 I*\/ 3 | / 9 I*\/ 9411 | ____ | \ 81 /| ____ | \ 81 /|| ____ | \ 81 /| ____ | \ 81 /| ________________
||- - - -------|*3 / - + ---------- | | ||- - - -------|*3 / - + ---------- | \/ 11 *cos|--------------| \/ 33 *sin|--------------|| \/ 11 *sin|--------------| \/ 33 *cos|--------------| ||- - + -------|*3 / - + ---------- | | ||- - + -------|*3 / - + ---------- | \/ 11 *cos|--------------| \/ 33 *sin|--------------|| \/ 11 *sin|--------------| \/ 33 *cos|--------------| / ______
\\ 2 2 / \/ 2 18 / | \\ 2 2 / \/ 2 18 / \ 3 / \ 3 /| \ 3 / \ 3 / \\ 2 2 / \/ 2 18 / | \\ 2 2 / \/ 2 18 / \ 3 / \ 3 /| \ 3 / \ 3 / / 9 I*\/ 9411 11
-------------------------------------------- + I*|-------------------------------------------- - -------------------------- - --------------------------| + -------------------------- - -------------------------- + -------------------------------------------- + I*|-------------------------------------------- + -------------------------- - --------------------------| - -------------------------- - -------------------------- + 3 / - + ---------- + -----------------------
3 \ 3 2 6 / 2 6 3 \ 3 2 6 / 2 6 \/ 2 18 ________________
/ ______
/ 9 I*\/ 9411
3*3 / - + ----------
\/ 2 18
$$\left(\frac{11}{3 \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}} + \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}\right) + \left(\left(\frac{11 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} - \frac{\sqrt{33} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} - \frac{\sqrt{11} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} + i \left(\frac{11 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} - \frac{\sqrt{33} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{\sqrt{11} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2}\right)\right) + \left(- \frac{\sqrt{33} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{11 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} + \frac{\sqrt{11} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{11} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} - \frac{\sqrt{33} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{11 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
11*re|-------------------------------------| 11*re|-------------------------------------| |11*im|-------------------------------------| / / ______\\ / / ______\\| |11*im|-------------------------------------| / / ______\\ / / ______\\| / / ______\\
| ________________| | ________________| | | ________________| | |\/ 9411 || | |\/ 9411 ||| | | ________________| | |\/ 9411 || | |\/ 9411 ||| | |\/ 9411 ||
|/ ___\ / ______ | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|--------|| |atan|--------||| | |/ ___\ / ______ | |atan|--------|| |atan|--------||| |atan|--------||
________________ || 1 I*\/ 3 | / 9 I*\/ 9411 | || 1 I*\/ 3 | / 9 I*\/ 9411 | | || 1 I*\/ 3 | / 9 I*\/ 9411 | ____ | \ 81 /| ____ | \ 81 /|| | || 1 I*\/ 3 | / 9 I*\/ 9411 | ____ | \ 81 /| ____ | \ 81 /|| ____ | \ 81 /|
/ ______ ||- - + -------|*3 / - + ---------- | ||- - - -------|*3 / - + ---------- | | ||- - + -------|*3 / - + ---------- | \/ 11 *cos|--------------| \/ 33 *sin|--------------|| | ||- - - -------|*3 / - + ---------- | \/ 11 *cos|--------------| \/ 33 *sin|--------------|| \/ 33 *cos|--------------|
/ 9 I*\/ 9411 11 \\ 2 2 / \/ 2 18 / \\ 2 2 / \/ 2 18 / | \\ 2 2 / \/ 2 18 / \ 3 / \ 3 /| | \\ 2 2 / \/ 2 18 / \ 3 / \ 3 /| \ 3 /
3 / - + ---------- + ----------------------- + -------------------------------------------- + -------------------------------------------- + I*|-------------------------------------------- + -------------------------- - --------------------------| + I*|-------------------------------------------- - -------------------------- - --------------------------| - --------------------------
\/ 2 18 ________________ 3 3 \ 3 2 6 / \ 3 2 6 / 3
/ ______
/ 9 I*\/ 9411
3*3 / - + ----------
\/ 2 18
$$- \frac{\sqrt{33} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{3} + \frac{11 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} + \frac{11 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} + \frac{11}{3 \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}} + i \left(- \frac{\sqrt{11} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} - \frac{\sqrt{33} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{11 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3}\right) + i \left(\frac{11 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} - \frac{\sqrt{33} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{\sqrt{11} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2}\right) + \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
|11*re|-------------------------------------| |11*im|-------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\| |11*re|-------------------------------------| |11*im|-------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\|
| | ________________| | | ________________| | |\/ 9411 || | |\/ 9411 ||| | |\/ 9411 || | |\/ 9411 ||| | | ________________| | | ________________| | |\/ 9411 || | |\/ 9411 ||| | |\/ 9411 || | |\/ 9411 |||
| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|--------|| |atan|--------||| |atan|--------|| |atan|--------||| | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|--------|| |atan|--------||| |atan|--------|| |atan|--------|||
| || 1 I*\/ 3 | / 9 I*\/ 9411 | | || 1 I*\/ 3 | / 9 I*\/ 9411 | ____ | \ 81 /| ____ | \ 81 /|| ____ | \ 81 /| ____ | \ 81 /|| | || 1 I*\/ 3 | / 9 I*\/ 9411 | | || 1 I*\/ 3 | / 9 I*\/ 9411 | ____ | \ 81 /| ____ | \ 81 /|| ____ | \ 81 /| ____ | \ 81 /|| / ________________ \
| ||- - - -------|*3 / - + ---------- | | ||- - - -------|*3 / - + ---------- | \/ 11 *cos|--------------| \/ 33 *sin|--------------|| \/ 11 *sin|--------------| \/ 33 *cos|--------------|| | ||- - + -------|*3 / - + ---------- | | ||- - + -------|*3 / - + ---------- | \/ 11 *cos|--------------| \/ 33 *sin|--------------|| \/ 11 *sin|--------------| \/ 33 *cos|--------------|| | / ______ |
| \\ 2 2 / \/ 2 18 / | \\ 2 2 / \/ 2 18 / \ 3 / \ 3 /| \ 3 / \ 3 /| | \\ 2 2 / \/ 2 18 / | \\ 2 2 / \/ 2 18 / \ 3 / \ 3 /| \ 3 / \ 3 /| | / 9 I*\/ 9411 11 |
|-------------------------------------------- + I*|-------------------------------------------- - -------------------------- - --------------------------| + -------------------------- - --------------------------|*|-------------------------------------------- + I*|-------------------------------------------- + -------------------------- - --------------------------| - -------------------------- - --------------------------|*|3 / - + ---------- + -----------------------|
\ 3 \ 3 2 6 / 2 6 / \ 3 \ 3 2 6 / 2 6 / |\/ 2 18 ________________|
| / ______ |
| / 9 I*\/ 9411 |
| 3*3 / - + ---------- |
\ \/ 2 18 /
$$\left(- \frac{\sqrt{33} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{11 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} + \frac{\sqrt{11} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{11} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} - \frac{\sqrt{33} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{11 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3}\right)\right) \left(\frac{11 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} - \frac{\sqrt{33} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} - \frac{\sqrt{11} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2} + i \left(\frac{11 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}}\right)}}{3} - \frac{\sqrt{33} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{6} + \frac{\sqrt{11} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}}{2}\right)\right) \left(\frac{11}{3 \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}} + \sqrt[3]{\frac{9}{2} + \frac{\sqrt{9411} i}{18}}\right)$$
=
/ / / ______\\\
| | |\/ 9411 |||
| |2*atan|--------||| / 2/3\
| | \ 81 /|| | 3 ____ 3 ____ / ______\ |
|-132 + 264*cos|----------------||*\22*\/ 18 + \/ 12 *\81 + I*\/ 9411 / /
\ \ 3 //
----------------------------------------------------------------------------
_________________
3 / ______
216*\/ 81 + I*\/ 9411
$$\frac{\left(-132 + 264 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{9411}}{81} \right)}}{3} \right)}\right) \left(22 \sqrt[3]{18} + \sqrt[3]{12} \left(81 + \sqrt{9411} i\right)^{\frac{2}{3}}\right)}{216 \sqrt[3]{81 + \sqrt{9411} i}}$$
(-132 + 264*cos(2*atan(sqrt(9411)/81)/3))*(22*18^(1/3) + 12^(1/3)*(81 + i*sqrt(9411))^(2/3))/(216*(81 + i*sqrt(9411))^(1/3))
Respuesta numérica
[src]
x1 = -0.880169656554596 - 0.e-22*i
x2 = -2.78775903903729 + 0.e-22*i
x3 = 3.66792869559189 - 0.e-21*i
x3 = 3.66792869559189 - 0.e-21*i