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- La ecuación:
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Ecuación 6*x^2+x-7=0
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Ecuación 2-5(3+2x)=17
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Ecuación (6*x+8)/2+5=5*x/3
- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
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- raíz cuadrada de (cuatro en el grado (cinco multiplicar por (x menos dos))) menos dieciséis en el grado (tres menos x) es igual a cero
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- sqrt(4^(5(x-2)))-16^(3-x)=0
- sqrt(4(5(x-2)))-16(3-x)=0
- sqrt45x-2-163-x=0
- sqrt4^5x-2-16^3-x=0
- sqrt(4^(5*(x-2)))-16^(3-x)=O
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Expresiones semejantes
- sqrt(4^(5*(x-2)))-16^(3+x)=0
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- sqrt(4^(5*(x-2)))+16^(3-x)=0
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Expresiones con funciones
- Raíz cuadrada sqrt
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- sqrt((1-a)^10)=(1-a)^5
- Sqrt(x^2-1)*sqrt(y^2-1)=a^2-1
- sqrt(4/3x-17)=1/2
sqrt(4^(5*(x-2)))-16^(3-x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
____________ / 5*(x - 2) 3 - x \/ 4 - 16 = 0
$$- 16^{3 - x} + \sqrt{4^{5 \left(x - 2\right)}} = 0$$
Respuesta rápida
[src]
x1 = 22/9
$$x_{1} = \frac{22}{9}$$
log(4194304) pi*I
x2 = ------------ - --------
9*log(2) 9*log(2)
$$x_{2} = \frac{\log{\left(4194304 \right)}}{9 \log{\left(2 \right)}} - \frac{i \pi}{9 \log{\left(2 \right)}}$$
log(4194304) pi*I
x3 = ------------ + --------
9*log(2) 9*log(2)
$$x_{3} = \frac{\log{\left(4194304 \right)}}{9 \log{\left(2 \right)}} + \frac{i \pi}{9 \log{\left(2 \right)}}$$
/ / /pi\\\
| |sin|--|||
| | \9 /||
I*|-pi + atan|-------||
| | /pi\||
| |cos|--|||
22 \ \ \9 ///
x4 = -- + -----------------------
9 log(2)
$$x_{4} = \frac{22}{9} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{9} \right)}}{\cos{\left(\frac{\pi}{9} \right)}} \right)}\right)}{\log{\left(2 \right)}}$$
/ / /pi\\\
| |cos|--|||
| | \18/||
/ _____________________\ I*|-pi + atan|-------||
| / 2/pi\ 2/pi\ | | | /pi\||
log| / cos |--| + sin |--| | | |sin|--|||
22 \\/ \18/ \18/ / \ \ \18///
x5 = -- + ------------------------------ + -----------------------
9 log(2) log(2)
$$x_{5} = \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{\log{\left(2 \right)}}$$
/ / /pi\\\
| |cos|--|||
| | \18/||
/ _____________________\ I*|pi - atan|-------||
| / 2/pi\ 2/pi\ | | | /pi\||
log| / cos |--| + sin |--| | | |sin|--|||
22 \\/ \18/ \18/ / \ \ \18///
x6 = -- + ------------------------------ + ----------------------
9 log(2) log(2)
$$x_{6} = \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{\log{\left(2 \right)}}$$
/ /pi\\
|cos|--||
| \18/|
/ _____________________\ I*atan|-------|
| / 2/pi\ 2/pi\ | | /pi\|
log| / cos |--| + sin |--| | |sin|--||
22 \\/ \18/ \18/ / \ \18//
x7 = -- + ------------------------------ - ---------------
9 log(2) log(2)
$$x_{7} = \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} - \frac{i \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}}$$
/ /pi\\
|cos|--||
| \18/|
/ _____________________\ I*atan|-------|
| / 2/pi\ 2/pi\ | | /pi\|
log| / cos |--| + sin |--| | |sin|--||
22 \\/ \18/ \18/ / \ \18//
x8 = -- + ------------------------------ + ---------------
9 log(2) log(2)
$$x_{8} = \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}}$$
22 8*pi*I
x9 = -- + --------
9 9*log(2)
$$x_{9} = \frac{22}{9} + \frac{8 i \pi}{9 \log{\left(2 \right)}}$$
22 pi*I
x10 = -- + ------
9 log(2)
$$x_{10} = \frac{22}{9} + \frac{i \pi}{\log{\left(2 \right)}}$$
x10 = 22/9 + i*pi/log(2)
Suma y producto de raíces
[src]
suma
/ / /pi\\\ / / /pi\\\ / / /pi\\\ / /pi\\ / /pi\\
| |sin|--||| | |cos|--||| | |cos|--||| |cos|--|| |cos|--||
| | \9 /|| | | \18/|| | | \18/|| | \18/| | \18/|
I*|-pi + atan|-------|| / _____________________\ I*|-pi + atan|-------|| / _____________________\ I*|pi - atan|-------|| / _____________________\ I*atan|-------| / _____________________\ I*atan|-------|
| | /pi\|| | / 2/pi\ 2/pi\ | | | /pi\|| | / 2/pi\ 2/pi\ | | | /pi\|| | / 2/pi\ 2/pi\ | | /pi\| | / 2/pi\ 2/pi\ | | /pi\|
| |cos|--||| log| / cos |--| + sin |--| | | |sin|--||| log| / cos |--| + sin |--| | | |sin|--||| log| / cos |--| + sin |--| | |sin|--|| log| / cos |--| + sin |--| | |sin|--||
22 log(4194304) pi*I log(4194304) pi*I 22 \ \ \9 /// 22 \\/ \18/ \18/ / \ \ \18/// 22 \\/ \18/ \18/ / \ \ \18/// 22 \\/ \18/ \18/ / \ \18// 22 \\/ \18/ \18/ / \ \18// 22 8*pi*I 22 pi*I
-- + ------------ - -------- + ------------ + -------- + -- + ----------------------- + -- + ------------------------------ + ----------------------- + -- + ------------------------------ + ---------------------- + -- + ------------------------------ - --------------- + -- + ------------------------------ + --------------- + -- + -------- + -- + ------
9 9*log(2) 9*log(2) 9*log(2) 9*log(2) 9 log(2) 9 log(2) log(2) 9 log(2) log(2) 9 log(2) log(2) 9 log(2) log(2) 9 9*log(2) 9 log(2)
$$\left(\left(\left(\left(\left(\left(\left(\frac{22}{9} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{9} \right)}}{\cos{\left(\frac{\pi}{9} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) + \left(\left(\frac{22}{9} + \left(\frac{\log{\left(4194304 \right)}}{9 \log{\left(2 \right)}} - \frac{i \pi}{9 \log{\left(2 \right)}}\right)\right) + \left(\frac{\log{\left(4194304 \right)}}{9 \log{\left(2 \right)}} + \frac{i \pi}{9 \log{\left(2 \right)}}\right)\right)\right) + \left(\frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right)\right) + \left(\frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right)\right) + \left(\frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} - \frac{i \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}}\right)\right) + \left(\frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}}\right)\right) + \left(\frac{22}{9} + \frac{8 i \pi}{9 \log{\left(2 \right)}}\right)\right) + \left(\frac{22}{9} + \frac{i \pi}{\log{\left(2 \right)}}\right)$$
=
/ / /pi\\\ / / /pi\\\ / / /pi\\\
| |cos|--||| | |sin|--||| | |cos|--|||
| | \18/|| | | \9 /|| | | \18/||
/ _____________________\ I*|pi - atan|-------|| I*|-pi + atan|-------|| I*|-pi + atan|-------||
| / 2/pi\ 2/pi\ | | | /pi\|| | | /pi\|| | | /pi\||
4*log| / cos |--| + sin |--| | | |sin|--||| | |cos|--||| | |sin|--|||
176 \\/ \18/ \18/ / 2*log(4194304) \ \ \18/// \ \ \9 /// \ \ \18/// 17*pi*I
--- + -------------------------------- + -------------- + ---------------------- + ----------------------- + ----------------------- + --------
9 log(2) 9*log(2) log(2) log(2) log(2) 9*log(2)
$$\frac{4 \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{2 \log{\left(4194304 \right)}}{9 \log{\left(2 \right)}} + \frac{176}{9} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{9} \right)}}{\cos{\left(\frac{\pi}{9} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{17 i \pi}{9 \log{\left(2 \right)}}$$
producto
/ / / /pi\\\\ / / / /pi\\\\ / / / /pi\\\\ / / /pi\\\ / / /pi\\\
| | |sin|--|||| | | |cos|--|||| | | |cos|--|||| | |cos|--||| | |cos|--|||
| | | \9 /||| | | | \18/||| | | | \18/||| | | \18/|| | | \18/||
| I*|-pi + atan|-------||| | / _____________________\ I*|-pi + atan|-------||| | / _____________________\ I*|pi - atan|-------||| | / _____________________\ I*atan|-------|| | / _____________________\ I*atan|-------||
/log(4194304) pi*I \ | | | /pi\||| | | / 2/pi\ 2/pi\ | | | /pi\||| | | / 2/pi\ 2/pi\ | | | /pi\||| | | / 2/pi\ 2/pi\ | | /pi\|| | | / 2/pi\ 2/pi\ | | /pi\||
22*|------------ - --------| | | |cos|--|||| | log| / cos |--| + sin |--| | | |sin|--|||| | log| / cos |--| + sin |--| | | |sin|--|||| | log| / cos |--| + sin |--| | |sin|--||| | log| / cos |--| + sin |--| | |sin|--|||
\ 9*log(2) 9*log(2)/ /log(4194304) pi*I \ |22 \ \ \9 ///| |22 \\/ \18/ \18/ / \ \ \18///| |22 \\/ \18/ \18/ / \ \ \18///| |22 \\/ \18/ \18/ / \ \18//| |22 \\/ \18/ \18/ / \ \18//| /22 8*pi*I \ /22 pi*I \
----------------------------*|------------ + --------|*|-- + -----------------------|*|-- + ------------------------------ + -----------------------|*|-- + ------------------------------ + ----------------------|*|-- + ------------------------------ - ---------------|*|-- + ------------------------------ + ---------------|*|-- + --------|*|-- + ------|
9 \ 9*log(2) 9*log(2)/ \9 log(2) / \9 log(2) log(2) / \9 log(2) log(2) / \9 log(2) log(2) / \9 log(2) log(2) / \9 9*log(2)/ \9 log(2)/
$$\frac{22 \left(\frac{\log{\left(4194304 \right)}}{9 \log{\left(2 \right)}} - \frac{i \pi}{9 \log{\left(2 \right)}}\right)}{9} \left(\frac{\log{\left(4194304 \right)}}{9 \log{\left(2 \right)}} + \frac{i \pi}{9 \log{\left(2 \right)}}\right) \left(\frac{22}{9} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{9} \right)}}{\cos{\left(\frac{\pi}{9} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(\frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(\frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(\frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} - \frac{i \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}}\right) \left(\frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{22}{9} + \frac{i \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}}{\log{\left(2 \right)}}\right) \left(\frac{22}{9} + \frac{8 i \pi}{9 \log{\left(2 \right)}}\right) \left(\frac{22}{9} + \frac{i \pi}{\log{\left(2 \right)}}\right)$$
=
88*(pi*I + log(4194304))*(-pi*I + log(4194304))*(-5*pi*I + log(4194304))*(-4*pi*I + log(2048))*(-4*pi*I + log(4194304))*(4*pi*I + log(2048))*(4*pi*I + log(4194304))*(5*pi*I + log(4194304))*(9*pi*I + log(4194304))
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
9
3486784401*log (2)
$$\frac{88 \left(\log{\left(2048 \right)} - 4 i \pi\right) \left(\log{\left(2048 \right)} + 4 i \pi\right) \left(\log{\left(4194304 \right)} - 5 i \pi\right) \left(\log{\left(4194304 \right)} - 4 i \pi\right) \left(\log{\left(4194304 \right)} - i \pi\right) \left(\log{\left(4194304 \right)} + i \pi\right) \left(\log{\left(4194304 \right)} + 4 i \pi\right) \left(\log{\left(4194304 \right)} + 5 i \pi\right) \left(\log{\left(4194304 \right)} + 9 i \pi\right)}{3486784401 \log{\left(2 \right)}^{9}}$$
88*(pi*i + log(4194304))*(-pi*i + log(4194304))*(-5*pi*i + log(4194304))*(-4*pi*i + log(2048))*(-4*pi*i + log(4194304))*(4*pi*i + log(2048))*(4*pi*i + log(4194304))*(5*pi*i + log(4194304))*(9*pi*i + log(4194304))/(3486784401*log(2)^9)
Respuesta numérica
[src]
x1 = 2.44444444444444
x2 = 2.44444444444444 - 0.503595571314133*i
x3 = 2.44444444444444 + 0.503595571314133*i
x4 = 2.44444444444444 - 4.02876457051306*i
x5 = 2.44444444444444 - 2.51797785657066*i
x6 = 2.44444444444444 + 2.51797785657066*i
x7 = 2.44444444444444 - 2.01438228525653*i
x8 = 2.44444444444444 + 2.01438228525653*i
x9 = 2.44444444444444 + 4.02876457051306*i
x10 = 2.44444444444444 + 4.53236014182719*i
x10 = 2.44444444444444 + 4.53236014182719*i