6÷(3x+6)+(x+1÷(x+3))=2 la ecuación
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Solución
Gráfica
/ 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 /
x1=−1−33cos(3atan(9687))+34re((−21−23i)321+18687i1)+sin3atan(9687)+i−cos3atan(9687)−33sin(3atan(9687))+34im((−21−23i)321+18687i1)
/ 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
x2=−1+34re((−21+23i)321+18687i1)−33cos(3atan(9687))−sin3atan(9687)+i34im((−21+23i)321+18687i1)−33sin(3atan(9687))+cos3atan(9687)
_______________
/ _____
/ 1 I*\/ 687 4
x3 = -1 + 3 / - + --------- + ----------------------
\/ 2 18 _______________
/ _____
/ 1 I*\/ 687
3*3 / - + ---------
\/ 2 18
x3=−1+3321+18687i4+321+18687i
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]
/ 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
−1+3321+18687i4+321+18687i+−1+34re((−21+23i)321+18687i1)−33cos(3atan(9687))−sin3atan(9687)+i34im((−21+23i)321+18687i1)−33sin(3atan(9687))+cos3atan(9687)+−1−33cos(3atan(9687))+34re((−21−23i)321+18687i1)+sin3atan(9687)+i−cos3atan(9687)−33sin(3atan(9687))+34im((−21−23i)321+18687i1)
/ 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
−3−323cos(3atan(9687))+34re((−21+23i)321+18687i1)+34re((−21−23i)321+18687i1)+3321+18687i4+i−cos3atan(9687)−33sin(3atan(9687))+34im((−21−23i)321+18687i1)+i34im((−21+23i)321+18687i1)−33sin(3atan(9687))+cos3atan(9687)+321+18687i
/ / 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 /
−1−33cos(3atan(9687))+34re((−21−23i)321+18687i1)+sin3atan(9687)+i−cos3atan(9687)−33sin(3atan(9687))+34im((−21−23i)321+18687i1)−1+34re((−21+23i)321+18687i1)−33cos(3atan(9687))−sin3atan(9687)+i34im((−21+23i)321+18687i1)−33sin(3atan(9687))+cos3atan(9687)−1+3321+18687i4+321+18687i
/ / / _____\\ / / _____\\\
| | |\/ 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 //
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_______________
3 / _____
54*\/ 9 + I*\/ 687
5439+687i(8318+(−6+3108+12687i)39+687i)(−3+24cos(32atan(9687))+123cos(3atan(9687)))
(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))
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