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Ecuación 3*x^2-x+2=0
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Ecuación 1-x/2=x/3
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Ecuación 3*x^2-9=0
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Ecuación 0,084:(6,2-x)=1,2
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Expresiones idénticas
- seis ÷(tres x+ seis)+(x+ uno ÷(x+3))= dos
- 6÷(3x más 6) más (x más 1÷(x más 3)) es igual a 2
- seis ÷(tres x más seis) más (x más uno ÷(x más 3)) es igual a dos
- 6÷3x+6+x+1÷x+3=2
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Expresiones semejantes
- 6÷(3x+6)-(x+1÷(x+3))=2
- 6÷(3x+6)+(x+1÷(x-3))=2
- 6÷(3x-6)+(x+1÷(x+3))=2
- 6÷(3x+6)+(x-1÷(x+3))=2
6÷(3x+6)+(x+1÷(x+3))=2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
6 1 ------- + x + ----- = 2 3*x + 6 x + 3
$$\left(x + \frac{1}{x + 3}\right) + \frac{6}{3 x + 6} = 2$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
4*re|------------------------------------| | 4*im|------------------------------------| / / _____\\| / / _____\\
| _______________ | | | _______________ | | |\/ 687 ||| | |\/ 687 ||
| / _____ / ___\| | / / _____\\ | / _____ / ___\| |atan|-------||| |atan|-------|| / / _____\\
| / 1 I*\/ 687 | 1 I*\/ 3 || | | |\/ 687 || | / 1 I*\/ 687 | 1 I*\/ 3 || ___ | \ 9 /|| ___ | \ 9 /| | |\/ 687 ||
|3 / - + --------- *|- - - -------|| | |atan|-------|| |3 / - + --------- *|- - - -------|| \/ 3 *sin|-------------|| \/ 3 *cos|-------------| |atan|-------||
\\/ 2 18 \ 2 2 // | | \ 9 /| \\/ 2 18 \ 2 2 // \ 3 /| \ 3 / | \ 9 /|
x1 = -1 + ------------------------------------------ + I*|- cos|-------------| + ------------------------------------------ - ------------------------| - ------------------------ + sin|-------------|
3 \ \ 3 / 3 3 / 3 \ 3 /
$$x_{1} = -1 - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \frac{4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} + \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} + i \left(- \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \frac{4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3}\right)$$
/ 1 \ / / 1 \ \
4*re|------------------------------------| |4*im|------------------------------------| / / _____\\ | / / _____\\
| _______________ | | | _______________ | | |\/ 687 || | | |\/ 687 ||
/ / _____\\ | / _____ / ___\| | | / _____ / ___\| |atan|-------|| / / _____\\| |atan|-------||
| |\/ 687 || | / 1 I*\/ 687 | 1 I*\/ 3 || | | / 1 I*\/ 687 | 1 I*\/ 3 || ___ | \ 9 /| | |\/ 687 ||| ___ | \ 9 /|
|atan|-------|| |3 / - + --------- *|- - + -------|| | |3 / - + --------- *|- - + -------|| \/ 3 *sin|-------------| |atan|-------||| \/ 3 *cos|-------------|
| \ 9 /| \\/ 2 18 \ 2 2 // | \\/ 2 18 \ 2 2 // \ 3 / | \ 9 /|| \ 3 /
x2 = -1 - sin|-------------| + ------------------------------------------ + I*|------------------------------------------ - ------------------------ + cos|-------------|| - ------------------------
\ 3 / 3 \ 3 3 \ 3 // 3
$$x_{2} = -1 + \frac{4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} + i \left(\frac{4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}\right)$$
_______________
/ _____
/ 1 I*\/ 687 4
x3 = -1 + 3 / - + --------- + ----------------------
\/ 2 18 _______________
/ _____
/ 1 I*\/ 687
3*3 / - + ---------
\/ 2 18
$$x_{3} = -1 + \frac{4}{3 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}$$
x3 = -1 + 4/(3*(1/2 + sqrt(687)*i/18)^(1/3)) + (1/2 + sqrt(687)*i/18)^(1/3)
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
4*re|------------------------------------| | 4*im|------------------------------------| / / _____\\| / / _____\\ 4*re|------------------------------------| |4*im|------------------------------------| / / _____\\ | / / _____\\
| _______________ | | | _______________ | | |\/ 687 ||| | |\/ 687 || | _______________ | | | _______________ | | |\/ 687 || | | |\/ 687 ||
| / _____ / ___\| | / / _____\\ | / _____ / ___\| |atan|-------||| |atan|-------|| / / _____\\ / / _____\\ | / _____ / ___\| | | / _____ / ___\| |atan|-------|| / / _____\\| |atan|-------||
| / 1 I*\/ 687 | 1 I*\/ 3 || | | |\/ 687 || | / 1 I*\/ 687 | 1 I*\/ 3 || ___ | \ 9 /|| ___ | \ 9 /| | |\/ 687 || | |\/ 687 || | / 1 I*\/ 687 | 1 I*\/ 3 || | | / 1 I*\/ 687 | 1 I*\/ 3 || ___ | \ 9 /| | |\/ 687 ||| ___ | \ 9 /| _______________
|3 / - + --------- *|- - - -------|| | |atan|-------|| |3 / - + --------- *|- - - -------|| \/ 3 *sin|-------------|| \/ 3 *cos|-------------| |atan|-------|| |atan|-------|| |3 / - + --------- *|- - + -------|| | |3 / - + --------- *|- - + -------|| \/ 3 *sin|-------------| |atan|-------||| \/ 3 *cos|-------------| / _____
\\/ 2 18 \ 2 2 // | | \ 9 /| \\/ 2 18 \ 2 2 // \ 3 /| \ 3 / | \ 9 /| | \ 9 /| \\/ 2 18 \ 2 2 // | \\/ 2 18 \ 2 2 // \ 3 / | \ 9 /|| \ 3 / / 1 I*\/ 687 4
-1 + ------------------------------------------ + I*|- cos|-------------| + ------------------------------------------ - ------------------------| - ------------------------ + sin|-------------| + -1 - sin|-------------| + ------------------------------------------ + I*|------------------------------------------ - ------------------------ + cos|-------------|| - ------------------------ + -1 + 3 / - + --------- + ----------------------
3 \ \ 3 / 3 3 / 3 \ 3 / \ 3 / 3 \ 3 3 \ 3 // 3 \/ 2 18 _______________
/ _____
/ 1 I*\/ 687
3*3 / - + ---------
\/ 2 18
$$\left(-1 + \frac{4}{3 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}\right) + \left(\left(-1 + \frac{4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} + i \left(\frac{4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}\right)\right) + \left(-1 - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \frac{4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} + \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} + i \left(- \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \frac{4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
4*re|------------------------------------| 4*re|------------------------------------| | 4*im|------------------------------------| / / _____\\| |4*im|------------------------------------| / / _____\\ | / / _____\\
| _______________ | | _______________ | | | _______________ | | |\/ 687 ||| | | _______________ | | |\/ 687 || | | |\/ 687 ||
| / _____ / ___\| | / _____ / ___\| | / / _____\\ | / _____ / ___\| |atan|-------||| | | / _____ / ___\| |atan|-------|| / / _____\\| |atan|-------||
_______________ | / 1 I*\/ 687 | 1 I*\/ 3 || | / 1 I*\/ 687 | 1 I*\/ 3 || | | |\/ 687 || | / 1 I*\/ 687 | 1 I*\/ 3 || ___ | \ 9 /|| | | / 1 I*\/ 687 | 1 I*\/ 3 || ___ | \ 9 /| | |\/ 687 ||| ___ | \ 9 /|
/ _____ |3 / - + --------- *|- - + -------|| |3 / - + --------- *|- - - -------|| | |atan|-------|| |3 / - + --------- *|- - - -------|| \/ 3 *sin|-------------|| | |3 / - + --------- *|- - + -------|| \/ 3 *sin|-------------| |atan|-------||| 2*\/ 3 *cos|-------------|
/ 1 I*\/ 687 4 \\/ 2 18 \ 2 2 // \\/ 2 18 \ 2 2 // | | \ 9 /| \\/ 2 18 \ 2 2 // \ 3 /| | \\/ 2 18 \ 2 2 // \ 3 / | \ 9 /|| \ 3 /
-3 + 3 / - + --------- + ---------------------- + ------------------------------------------ + ------------------------------------------ + I*|- cos|-------------| + ------------------------------------------ - ------------------------| + I*|------------------------------------------ - ------------------------ + cos|-------------|| - --------------------------
\/ 2 18 _______________ 3 3 \ \ 3 / 3 3 / \ 3 3 \ 3 // 3
/ _____
/ 1 I*\/ 687
3*3 / - + ---------
\/ 2 18
$$-3 - \frac{2 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \frac{4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} + \frac{4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} + \frac{4}{3 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}} + i \left(- \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \frac{4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3}\right) + i \left(\frac{4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}\right) + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 4*re|------------------------------------| | 4*im|------------------------------------| / / _____\\| / / _____\\ | | 4*re|------------------------------------| |4*im|------------------------------------| / / _____\\ | / / _____\\|
| | _______________ | | | _______________ | | |\/ 687 ||| | |\/ 687 || | | | _______________ | | | _______________ | | |\/ 687 || | | |\/ 687 |||
| | / _____ / ___\| | / / _____\\ | / _____ / ___\| |atan|-------||| |atan|-------|| / / _____\\| | / / _____\\ | / _____ / ___\| | | / _____ / ___\| |atan|-------|| / / _____\\| |atan|-------|||
| | / 1 I*\/ 687 | 1 I*\/ 3 || | | |\/ 687 || | / 1 I*\/ 687 | 1 I*\/ 3 || ___ | \ 9 /|| ___ | \ 9 /| | |\/ 687 ||| | | |\/ 687 || | / 1 I*\/ 687 | 1 I*\/ 3 || | | / 1 I*\/ 687 | 1 I*\/ 3 || ___ | \ 9 /| | |\/ 687 ||| ___ | \ 9 /|| / _______________ \
| |3 / - + --------- *|- - - -------|| | |atan|-------|| |3 / - + --------- *|- - - -------|| \/ 3 *sin|-------------|| \/ 3 *cos|-------------| |atan|-------||| | |atan|-------|| |3 / - + --------- *|- - + -------|| | |3 / - + --------- *|- - + -------|| \/ 3 *sin|-------------| |atan|-------||| \/ 3 *cos|-------------|| | / _____ |
| \\/ 2 18 \ 2 2 // | | \ 9 /| \\/ 2 18 \ 2 2 // \ 3 /| \ 3 / | \ 9 /|| | | \ 9 /| \\/ 2 18 \ 2 2 // | \\/ 2 18 \ 2 2 // \ 3 / | \ 9 /|| \ 3 /| | / 1 I*\/ 687 4 |
|-1 + ------------------------------------------ + I*|- cos|-------------| + ------------------------------------------ - ------------------------| - ------------------------ + sin|-------------||*|-1 - sin|-------------| + ------------------------------------------ + I*|------------------------------------------ - ------------------------ + cos|-------------|| - ------------------------|*|-1 + 3 / - + --------- + ----------------------|
\ 3 \ \ 3 / 3 3 / 3 \ 3 // \ \ 3 / 3 \ 3 3 \ 3 // 3 / | \/ 2 18 _______________|
| / _____ |
| / 1 I*\/ 687 |
| 3*3 / - + --------- |
\ \/ 2 18 /
$$\left(-1 - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \frac{4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} + \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} + i \left(- \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \frac{4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3}\right)\right) \left(-1 + \frac{4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} + i \left(\frac{4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}}{3} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}\right)\right) \left(-1 + \frac{4}{3 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}\right)$$
=
/ / / _____\\ / / _____\\\
| | |\/ 687 || | |\/ 687 |||
/ _______________ / ____________________\\ | |2*atan|-------|| |atan|-------|||
| 3 ____ 3 / _____ | 3 / _____ || | | \ 9 /| ___ | \ 9 /||
\8*\/ 18 + \/ 9 + I*\/ 687 *\-6 + \/ 108 + 12*I*\/ 687 //*|-3 + 24*cos|---------------| + 12*\/ 3 *cos|-------------||
\ \ 3 / \ 3 //
---------------------------------------------------------------------------------------------------------------------------
_______________
3 / _____
54*\/ 9 + I*\/ 687
$$\frac{\left(8 \sqrt[3]{18} + \left(-6 + \sqrt[3]{108 + 12 \sqrt{687} i}\right) \sqrt[3]{9 + \sqrt{687} i}\right) \left(-3 + 24 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)} + 12 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{687}}{9} \right)}}{3} \right)}\right)}{54 \sqrt[3]{9 + \sqrt{687} i}}$$
(8*18^(1/3) + (9 + i*sqrt(687))^(1/3)*(-6 + (108 + 12*i*sqrt(687))^(1/3)))*(-3 + 24*cos(2*atan(sqrt(687)/9)/3) + 12*sqrt(3)*cos(atan(sqrt(687)/9)/3))/(54*(9 + i*sqrt(687))^(1/3))
Respuesta numérica
[src]
x1 = -1.25410168836505 + 0.e-20*i
x2 = -2.8608058531117 + 0.e-23*i
x3 = 1.11490754147676 - 0.e-22*i
x3 = 1.11490754147676 - 0.e-22*i