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- La ecuación:
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Ecuación x^3
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Ecuación x+357=642
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Ecuación 4*x-4=12
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Ecuación 3x+1=-2
- Expresar {x} en función de y en la ecuación:
- 9*x+7*y=4
- 2*x+5*y=1
- -1*x+11*y=16
- -3*x-9*y=16
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Expresiones idénticas
- (sesenta y cuatro)^(dos -x)=(treinta y dos)^(x+ tres)
- (64) en el grado (2 menos x) es igual a (32) en el grado (x más 3)
- (sesenta y cuatro) en el grado (dos menos x) es igual a (treinta y dos) en el grado (x más tres)
- (64)(2-x)=(32)(x+3)
- 642-x=32x+3
- 64^2-x=32^x+3
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Expresiones semejantes
- (64)^(2+x)=(32)^(x+3)
- (64)^(2-x)=(32)^(x-3)
(64)^(2-x)=(32)^(x+3) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Suma y producto de raíces
[src]
suma
/ / /3*pi\\\ / / /pi\\\ / / /pi\\\ / / /pi\\\ / / /5*pi\\\
| |sin|----||| | |sin|--||| | |cos|--||| | |cos|--||| | |cos|----|||
| | \ 11 /|| | | \11/|| | | \22/|| | | \22/|| | | \ 22 /||
/ 8/11\ I*|pi - atan|---------|| I*|-pi + atan|-------|| / _____________________\ I*|-pi + atan|-------|| / _____________________\ I*|pi - atan|-------|| / _________________________\ I*|-pi + atan|---------||
|2 | | | /3*pi\|| | | /pi\|| | / 2/pi\ 2/pi\ | | | /pi\|| | / 2/pi\ 2/pi\ | | | /pi\|| | / 2/5*pi\ 2/5*pi\ | | | /5*pi\||
log|-----| | |cos|----||| | |cos|--||| log| / cos |--| + sin |--| | | |sin|--||| log| / cos |--| + sin |--| | | |sin|--||| log| / cos |----| + sin |----| | | |sin|----|||
3 log(8) 2*pi*I log(8) 4*pi*I log(8) 2*pi*I log(8) 4*pi*I \ 2 / \ \ \ 11 /// 3 \ \ \11/// 3 \\/ \22/ \22/ / \ \ \22/// 3 \\/ \22/ \22/ / \ \ \22/// 3 \\/ \ 22 / \ 22 / / \ \ \ 22 /// 3 10*pi*I
- -- + - --------- + --------- + - --------- + --------- + - --------- - --------- + - --------- - --------- + ---------- + ------------------------ + - -- + ----------------------- + - -- + ------------------------------ + ----------------------- + - -- + ------------------------------ + ---------------------- + - -- + ---------------------------------- + ------------------------- + - -- + ---------
11 11*log(2) 11*log(2) 11*log(2) 11*log(2) 11*log(2) 11*log(2) 11*log(2) 11*log(2) log(2) log(2) 11 log(2) 11 log(2) log(2) 11 log(2) log(2) 11 log(2) log(2) 11 11*log(2)
$$\left(\left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{5 \pi}{22} \right)} + \cos^{2}{\left(\frac{5 \pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{5 \pi}{22} \right)}}{\sin{\left(\frac{5 \pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) + \left(\left(\left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) + \left(\left(- \frac{3}{11} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{11} \right)}}{\cos{\left(\frac{\pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) + \left(\left(\left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{4 i \pi}{11 \log{\left(2 \right)}}\right) + \left(\left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{2 i \pi}{11 \log{\left(2 \right)}}\right) + \left(\left(- \frac{3}{11} + \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{2 i \pi}{11 \log{\left(2 \right)}}\right)\right) + \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{4 i \pi}{11 \log{\left(2 \right)}}\right)\right)\right)\right) + \left(\frac{\log{\left(\frac{2^{\frac{8}{11}}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{11} \right)}}{\cos{\left(\frac{3 \pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right)\right)\right)\right) + \left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right)\right)\right) + \left(- \frac{3}{11} + \frac{10 i \pi}{11 \log{\left(2 \right)}}\right)$$
=
/ / /3*pi\\\ / / /pi\\\ / / /pi\\\ / / /pi\\\ / / /5*pi\\\
| |sin|----||| | |cos|--||| | |sin|--||| | |cos|--||| | |cos|----|||
| | \ 11 /|| | | \22/|| | | \11/|| | | \22/|| | | \ 22 /||
/ _________________________\ / 8/11\ / _____________________\ I*|pi - atan|---------|| I*|pi - atan|-------|| I*|-pi + atan|-------|| I*|-pi + atan|-------|| I*|-pi + atan|---------||
| / 2/5*pi\ 2/5*pi\ | |2 | | / 2/pi\ 2/pi\ | | | /3*pi\|| | | /pi\|| | | /pi\|| | | /pi\|| | | /5*pi\||
log| / cos |----| + sin |----| | log|-----| 2*log| / cos |--| + sin |--| | | |cos|----||| | |sin|--||| | |cos|--||| | |sin|--||| | |sin|----|||
18 \\/ \ 22 / \ 22 / / \ 2 / \\/ \22/ \22/ / 4*log(8) \ \ \ 11 /// \ \ \22/// \ \ \11/// \ \ \22/// \ \ \ 22 /// 10*pi*I
- -- + ---------------------------------- + ---------- + -------------------------------- - --------- + ------------------------ + ---------------------- + ----------------------- + ----------------------- + ------------------------- + ---------
11 log(2) log(2) log(2) 11*log(2) log(2) log(2) log(2) log(2) log(2) 11*log(2)
$$- \frac{18}{11} - \frac{4 \log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{\log{\left(\frac{2^{\frac{8}{11}}}{2} \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{5 \pi}{22} \right)} + \cos^{2}{\left(\frac{5 \pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{2 \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{11} \right)}}{\cos{\left(\frac{\pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{5 \pi}{22} \right)}}{\sin{\left(\frac{5 \pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{11} \right)}}{\cos{\left(\frac{3 \pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{10 i \pi}{11 \log{\left(2 \right)}}$$
producto
/ / / /3*pi\\\\ / / / /pi\\\\ / / / /pi\\\\ / / / /pi\\\\ / / / /5*pi\\\\
| | |sin|----|||| | | |sin|--|||| | | |cos|--|||| | | |cos|--|||| | | |cos|----||||
| | | \ 11 /||| | | | \11/||| | | | \22/||| | | | \22/||| | | | \ 22 /|||
| / 8/11\ I*|pi - atan|---------||| | I*|-pi + atan|-------||| | / _____________________\ I*|-pi + atan|-------||| | / _____________________\ I*|pi - atan|-------||| | / _________________________\ I*|-pi + atan|---------|||
/ log(8) 2*pi*I \ | |2 | | | /3*pi\||| | | | /pi\||| | | / 2/pi\ 2/pi\ | | | /pi\||| | | / 2/pi\ 2/pi\ | | | /pi\||| | | / 2/5*pi\ 2/5*pi\ | | | /5*pi\|||
-3*|- --------- + ---------| |log|-----| | |cos|----|||| | | |cos|--|||| | log| / cos |--| + sin |--| | | |sin|--|||| | log| / cos |--| + sin |--| | | |sin|--|||| | log| / cos |----| + sin |----| | | |sin|----||||
\ 11*log(2) 11*log(2)/ / log(8) 4*pi*I \ / log(8) 2*pi*I \ / log(8) 4*pi*I \ | \ 2 / \ \ \ 11 ///| | 3 \ \ \11///| | 3 \\/ \22/ \22/ / \ \ \22///| | 3 \\/ \22/ \22/ / \ \ \22///| | 3 \\/ \ 22 / \ 22 / / \ \ \ 22 ///| / 3 10*pi*I \
----------------------------*|- --------- + ---------|*|- --------- - ---------|*|- --------- - ---------|*|---------- + ------------------------|*|- -- + -----------------------|*|- -- + ------------------------------ + -----------------------|*|- -- + ------------------------------ + ----------------------|*|- -- + ---------------------------------- + -------------------------|*|- -- + ---------|
11 \ 11*log(2) 11*log(2)/ \ 11*log(2) 11*log(2)/ \ 11*log(2) 11*log(2)/ \ log(2) log(2) / \ 11 log(2) / \ 11 log(2) log(2) / \ 11 log(2) log(2) / \ 11 log(2) log(2) / \ 11 11*log(2)/
$$- \frac{3 \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{2 i \pi}{11 \log{\left(2 \right)}}\right)}{11} \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{4 i \pi}{11 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{2 i \pi}{11 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{4 i \pi}{11 \log{\left(2 \right)}}\right) \left(\frac{\log{\left(\frac{2^{\frac{8}{11}}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{11} \right)}}{\cos{\left(\frac{3 \pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{11} \right)}}{\cos{\left(\frac{\pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{5 \pi}{22} \right)} + \cos^{2}{\left(\frac{5 \pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{5 \pi}{22} \right)}}{\sin{\left(\frac{5 \pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{10 i \pi}{11 \log{\left(2 \right)}}\right)$$
=
/ 10 10 2 8 4 6 6 4 8 2 \
-\177147*log (2) + 44236800*pi + 4330260*pi *log (2) + 35796816*pi *log (2) + 118895040*pi *log (2) + 145677312*pi *log (2)/
--------------------------------------------------------------------------------------------------------------------------------
10
285311670611*log (2)
$$- \frac{177147 \log{\left(2 \right)}^{10} + 4330260 \pi^{2} \log{\left(2 \right)}^{8} + 35796816 \pi^{4} \log{\left(2 \right)}^{6} + 118895040 \pi^{6} \log{\left(2 \right)}^{4} + 145677312 \pi^{8} \log{\left(2 \right)}^{2} + 44236800 \pi^{10}}{285311670611 \log{\left(2 \right)}^{10}}$$
-(177147*log(2)^10 + 44236800*pi^10 + 4330260*pi^2*log(2)^8 + 35796816*pi^4*log(2)^6 + 118895040*pi^6*log(2)^4 + 145677312*pi^8*log(2)^2)/(285311670611*log(2)^10)
Respuesta rápida
[src]
x1 = -3/11
$$x_{1} = - \frac{3}{11}$$
log(8) 2*pi*I
x2 = - --------- + ---------
11*log(2) 11*log(2)
$$x_{2} = - \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{2 i \pi}{11 \log{\left(2 \right)}}$$
log(8) 4*pi*I
x3 = - --------- + ---------
11*log(2) 11*log(2)
$$x_{3} = - \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{4 i \pi}{11 \log{\left(2 \right)}}$$
log(8) 2*pi*I
x4 = - --------- - ---------
11*log(2) 11*log(2)
$$x_{4} = - \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{2 i \pi}{11 \log{\left(2 \right)}}$$
log(8) 4*pi*I
x5 = - --------- - ---------
11*log(2) 11*log(2)
$$x_{5} = - \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{4 i \pi}{11 \log{\left(2 \right)}}$$
/ / /3*pi\\\
| |sin|----|||
| | \ 11 /||
/ 8/11\ I*|pi - atan|---------||
|2 | | | /3*pi\||
log|-----| | |cos|----|||
\ 2 / \ \ \ 11 ///
x6 = ---------- + ------------------------
log(2) log(2)
$$x_{6} = \frac{\log{\left(\frac{2^{\frac{8}{11}}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{11} \right)}}{\cos{\left(\frac{3 \pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}$$
/ / /pi\\\
| |sin|--|||
| | \11/||
I*|-pi + atan|-------||
| | /pi\||
| |cos|--|||
3 \ \ \11///
x7 = - -- + -----------------------
11 log(2)
$$x_{7} = - \frac{3}{11} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{11} \right)}}{\cos{\left(\frac{\pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}$$
/ / /pi\\\
| |cos|--|||
| | \22/||
/ _____________________\ I*|-pi + atan|-------||
| / 2/pi\ 2/pi\ | | | /pi\||
log| / cos |--| + sin |--| | | |sin|--|||
3 \\/ \22/ \22/ / \ \ \22///
x8 = - -- + ------------------------------ + -----------------------
11 log(2) log(2)
$$x_{8} = - \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}$$
/ / /pi\\\
| |cos|--|||
| | \22/||
/ _____________________\ I*|pi - atan|-------||
| / 2/pi\ 2/pi\ | | | /pi\||
log| / cos |--| + sin |--| | | |sin|--|||
3 \\/ \22/ \22/ / \ \ \22///
x9 = - -- + ------------------------------ + ----------------------
11 log(2) log(2)
$$x_{9} = - \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}$$
/ / /5*pi\\\
| |cos|----|||
| | \ 22 /||
/ _________________________\ I*|-pi + atan|---------||
| / 2/5*pi\ 2/5*pi\ | | | /5*pi\||
log| / cos |----| + sin |----| | | |sin|----|||
3 \\/ \ 22 / \ 22 / / \ \ \ 22 ///
x10 = - -- + ---------------------------------- + -------------------------
11 log(2) log(2)
$$x_{10} = - \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{5 \pi}{22} \right)} + \cos^{2}{\left(\frac{5 \pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{5 \pi}{22} \right)}}{\sin{\left(\frac{5 \pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}$$
3 10*pi*I
x11 = - -- + ---------
11 11*log(2)
$$x_{11} = - \frac{3}{11} + \frac{10 i \pi}{11 \log{\left(2 \right)}}$$
x11 = -3/11 + 10*i*pi/(11*log(2))
Respuesta numérica
[src]
x1 = -0.272727272727273
x2 = -0.272727272727273 + 0.824065480332217*i
x3 = -0.272727272727273 + 1.64813096066443*i
x4 = -0.272727272727273 - 0.824065480332217*i
x5 = -0.272727272727273 - 1.64813096066443*i
x6 = -0.272727272727273 + 3.29626192132887*i
x7 = -0.272727272727273 - 4.12032740166109*i
x8 = -0.272727272727273 - 2.47219644099665*i
x9 = -0.272727272727273 + 2.47219644099665*i
x10 = -0.272727272727273 - 3.29626192132887*i
x11 = -0.272727272727273 + 4.12032740166109*i
x11 = -0.272727272727273 + 4.12032740166109*i