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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 3*x-6=x+4
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Ecuación 3^x=-1
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Ecuación 9^x-8*3^x-9=0
- Expresar {x} en función de y en la ecuación:
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
- 6*x+17*y=-11
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Expresiones idénticas
- veinticinco ^(x- uno)+sqrt(uno /(veinticinco ^(- dos *x)))= cuatrocientos setenta y cinco +(uno / cinco)^(uno - dos *x)
- 25 en el grado (x menos 1) más raíz cuadrada de (1 dividir por (25 en el grado ( menos 2 multiplicar por x))) es igual a 475 más (1 dividir por 5) en el grado (1 menos 2 multiplicar por x)
- veinticinco en el grado (x menos uno) más raíz cuadrada de (uno dividir por (veinticinco en el grado ( menos dos multiplicar por x))) es igual a cuatrocientos setenta y cinco más (uno dividir por cinco) en el grado (uno menos dos multiplicar por x)
- 25^(x-1)+√(1/(25^(-2*x)))=475+(1/5)^(1-2*x)
- 25(x-1)+sqrt(1/(25(-2*x)))=475+(1/5)(1-2*x)
- 25x-1+sqrt1/25-2*x=475+1/51-2*x
- 25^(x-1)+sqrt(1/(25^(-2x)))=475+(1/5)^(1-2x)
- 25(x-1)+sqrt(1/(25(-2x)))=475+(1/5)(1-2x)
- 25x-1+sqrt1/25-2x=475+1/51-2x
- 25^x-1+sqrt1/25^-2x=475+1/5^1-2x
- 25^(x-1)+sqrt(1 dividir por (25^(-2*x)))=475+(1 dividir por 5)^(1-2*x)
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Expresiones semejantes
- 25^(x-1)+sqrt(1/(25^(-2*x)))=475-(1/5)^(1-2*x)
- 25^(x-1)+sqrt(1/(25^(-2*x)))=475+(1/5)^(1+2*x)
- 25^(x-1)+sqrt(1/(25^(2*x)))=475+(1/5)^(1-2*x)
- 25^(x-1)-sqrt(1/(25^(-2*x)))=475+(1/5)^(1-2*x)
- 25^(x+1)+sqrt(1/(25^(-2*x)))=475+(1/5)^(1-2*x)
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x+2)-sqrt(x-6)=2
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(5+2*x)=8+-sqrt(x-1)
- sqrt(4*x^2+4*x-6)=2
25^(x-1)+sqrt(1/(25^(-2*x)))=475+(1/5)^(1-2*x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
________
x - 1 / 1 -1 + 2*x
25 + / ------ = 475 + 5
/ -2*x
\/ 25
$$25^{x - 1} + \sqrt{\frac{1}{25^{- 2 x}}} = \left(\frac{1}{5}\right)^{1 - 2 x} + 475$$
Suma y producto de raíces
[src]
suma
/ 1 \ | ------| / _____\ | log(5)| /11875\ /11875\ |25*\/ 399 | |/ _____\ | log|-----| log|-----| log|----------| ||25*\/ 399 | | \ 29 / pi*I \ 29 / pi*I \ 21 / pi*I log||----------| | + ---------- - -------- + ---------- + -------- + --------------- + ------ \\ 21 / / 2*log(5) 2*log(5) 2*log(5) 2*log(5) log(5) log(5)
$$\left(\left(\log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{\log{\left(5 \right)}}} \right)} + \left(\frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} - \frac{i \pi}{2 \log{\left(5 \right)}}\right)\right) + \left(\frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} + \frac{i \pi}{2 \log{\left(5 \right)}}\right)\right) + \left(\frac{\log{\left(\frac{25 \sqrt{399}}{21} \right)}}{\log{\left(5 \right)}} + \frac{i \pi}{\log{\left(5 \right)}}\right)$$
=
/ 1 \
/ _____\ | ------|
/11875\ |25*\/ 399 | | log(5)|
log|-----| log|----------| |/ _____\ |
\ 29 / \ 21 / pi*I ||25*\/ 399 | |
---------- + --------------- + ------ + log||----------| |
log(5) log(5) log(5) \\ 21 / /
$$\frac{\log{\left(\frac{25 \sqrt{399}}{21} \right)}}{\log{\left(5 \right)}} + \log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{\log{\left(5 \right)}}} \right)} + \frac{\log{\left(\frac{11875}{29} \right)}}{\log{\left(5 \right)}} + \frac{i \pi}{\log{\left(5 \right)}}$$
producto
/ 1 \ | ------| / / _____\ \ | log(5)| / /11875\ \ / /11875\ \ | |25*\/ 399 | | |/ _____\ | |log|-----| | |log|-----| | |log|----------| | ||25*\/ 399 | | | \ 29 / pi*I | | \ 29 / pi*I | | \ 21 / pi*I | log||----------| |*|---------- - --------|*|---------- + --------|*|--------------- + ------| \\ 21 / / \ 2*log(5) 2*log(5)/ \ 2*log(5) 2*log(5)/ \ log(5) log(5)/
$$\left(\frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} - \frac{i \pi}{2 \log{\left(5 \right)}}\right) \log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{\log{\left(5 \right)}}} \right)} \left(\frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} + \frac{i \pi}{2 \log{\left(5 \right)}}\right) \left(\frac{\log{\left(\frac{25 \sqrt{399}}{21} \right)}}{\log{\left(5 \right)}} + \frac{i \pi}{\log{\left(5 \right)}}\right)$$
=
/ 1 \
| ---------|
| 4 |
| 4*log (5)|
/ / _____\\ |/ _____\ |
/ /11875\\ | |25*\/ 399 || / /11875\\ ||25*\/ 399 | |
|pi*I + log|-----||*|pi*I + log|----------||*|-pi*I + log|-----||*log||----------| |
\ \ 29 // \ \ 21 // \ \ 29 // \\ 21 / /
$$\left(\log{\left(\frac{11875}{29} \right)} - i \pi\right) \left(\log{\left(\frac{11875}{29} \right)} + i \pi\right) \left(\log{\left(\frac{25 \sqrt{399}}{21} \right)} + i \pi\right) \log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{4 \log{\left(5 \right)}^{4}}} \right)}$$
(pi*i + log(11875/29))*(pi*i + log(25*sqrt(399)/21))*(-pi*i + log(11875/29))*log((25*sqrt(399)/21)^(1/(4*log(5)^4)))
Respuesta rápida
[src]
/ 1 \
| ------|
| log(5)|
|/ _____\ |
||25*\/ 399 | |
x1 = log||----------| |
\\ 21 / /
$$x_{1} = \log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{\log{\left(5 \right)}}} \right)}$$
/11875\
log|-----|
\ 29 / pi*I
x2 = ---------- - --------
2*log(5) 2*log(5)
$$x_{2} = \frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} - \frac{i \pi}{2 \log{\left(5 \right)}}$$
/11875\
log|-----|
\ 29 / pi*I
x3 = ---------- + --------
2*log(5) 2*log(5)
$$x_{3} = \frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} + \frac{i \pi}{2 \log{\left(5 \right)}}$$
/ _____\
|25*\/ 399 |
log|----------|
\ 21 / pi*I
x4 = --------------- + ------
log(5) log(5)
$$x_{4} = \frac{\log{\left(\frac{25 \sqrt{399}}{21} \right)}}{\log{\left(5 \right)}} + \frac{i \pi}{\log{\left(5 \right)}}$$
x4 = log(25*sqrt(399)/21)/log(5) + i*pi/log(5)
Respuesta numérica
[src]
x1 = 1.86863213313383 - 0.975990632915586*i
x2 = 1.86863213313383 + 0.975990632915586*i
x3 = 1.9689073254135 + 1.95198126583117*i
x4 = 1.9689073254135
x4 = 1.9689073254135