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Ecuación x^2=4
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Ecuación x^x=2
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Ecuación 3x^2-18=0
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Ecuación x+6,2=-7,8
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -11*x-11*y=4
- -14*x+4*y=-16
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Expresiones idénticas
- dos ^((x+ tres)/x)+ ocho ^(dos /x)- veintisiete = cero
- 2 en el grado ((x más 3) dividir por x) más 8 en el grado (2 dividir por x) menos 27 es igual a 0
- dos en el grado ((x más tres) dividir por x) más ocho en el grado (dos dividir por x) menos veintisiete es igual a cero
- 2((x+3)/x)+8(2/x)-27=0
- 2x+3/x+82/x-27=0
- 2^x+3/x+8^2/x-27=0
- 2^((x+3)/x)+8^(2/x)-27=O
- 2^((x+3) dividir por x)+8^(2 dividir por x)-27=0
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Expresiones semejantes
- 2^((x-3)/x)+8^(2/x)-27=0
- 2^((x+3)/x)+8^(2/x)+27=0
- 2^((x+3)/x)-8^(2/x)-27=0
2^((x+3)/x)+8^(2/x)-27=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
x + 3 2 ----- - x x 2 + 8 - 27 = 0
$$\left(2^{\frac{x + 3}{x}} + 8^{\frac{2}{x}}\right) - 27 = 0$$
Respuesta rápida
[src]
3*log(2)
x1 = -----------------
/ ___\
log\-1 + 2*\/ 7 /
$$x_{1} = \frac{3 \log{\left(2 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}}$$
/ ___\
log(8)*log\-1 + 2*\/ 7 / 2*pi*I*log(8)
x2 = -------------------------- + --------------------------
2/ ___\ 2 2/ ___\ 2
log \-1 + 2*\/ 7 / + 4*pi log \-1 + 2*\/ 7 / + 4*pi
$$x_{2} = \frac{\log{\left(8 \right)} \log{\left(-1 + 2 \sqrt{7} \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}} + \frac{2 i \pi \log{\left(8 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}}$$
/ ___\
log(8)*log\-1 + 2*\/ 7 / 2*pi*I*log(8)
x3 = -------------------------- - --------------------------
2/ ___\ 2 2/ ___\ 2
log \-1 + 2*\/ 7 / + 4*pi log \-1 + 2*\/ 7 / + 4*pi
$$x_{3} = \frac{\log{\left(8 \right)} \log{\left(-1 + 2 \sqrt{7} \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}} - \frac{2 i \pi \log{\left(8 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}}$$
/ ___\
log(2)*log\1 + 2*\/ 7 / pi*I*log(2)
x4 = --------------------------- - -----------------------
/ 2/ ___\\ 2/ ___\
| 2 log \1 + 2*\/ 7 /| 2 log \1 + 2*\/ 7 /
3*|pi + -----------------| pi + -----------------
\ 9 / 9
$$x_{4} = \frac{\log{\left(2 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{3 \left(\frac{\log{\left(1 + 2 \sqrt{7} \right)}^{2}}{9} + \pi^{2}\right)} - \frac{i \pi \log{\left(2 \right)}}{\frac{\log{\left(1 + 2 \sqrt{7} \right)}^{2}}{9} + \pi^{2}}$$
/ ___\
log(8)*log\1 + 2*\/ 7 / pi*I*log(8)
x5 = ----------------------- + -----------------------
2 2/ ___\ 2 2/ ___\
pi + log \1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 /
$$x_{5} = \frac{\log{\left(8 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}} + \frac{i \pi \log{\left(8 \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}}$$
/ ___\
log(8)*log\1 + 2*\/ 7 / pi*I*log(8)
x6 = ----------------------- - -----------------------
2 2/ ___\ 2 2/ ___\
pi + log \1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 /
$$x_{6} = \frac{\log{\left(8 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}} - \frac{i \pi \log{\left(8 \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}}$$
x6 = log(8)*log(1 + 2*sqrt(7))/(log(1 + 2*sqrt(7))^2 + pi^2) - i*pi*log(8)/(log(1 + 2*sqrt(7))^2 + pi^2)
Suma y producto de raíces
[src]
suma
/ ___\ / ___\ / ___\ / ___\ / ___\
3*log(2) log(8)*log\-1 + 2*\/ 7 / 2*pi*I*log(8) log(8)*log\-1 + 2*\/ 7 / 2*pi*I*log(8) log(2)*log\1 + 2*\/ 7 / pi*I*log(2) log(8)*log\1 + 2*\/ 7 / pi*I*log(8) log(8)*log\1 + 2*\/ 7 / pi*I*log(8)
----------------- + -------------------------- + -------------------------- + -------------------------- - -------------------------- + --------------------------- - ----------------------- + ----------------------- + ----------------------- + ----------------------- - -----------------------
/ ___\ 2/ ___\ 2 2/ ___\ 2 2/ ___\ 2 2/ ___\ 2 / 2/ ___\\ 2/ ___\ 2 2/ ___\ 2 2/ ___\ 2 2/ ___\ 2 2/ ___\
log\-1 + 2*\/ 7 / log \-1 + 2*\/ 7 / + 4*pi log \-1 + 2*\/ 7 / + 4*pi log \-1 + 2*\/ 7 / + 4*pi log \-1 + 2*\/ 7 / + 4*pi | 2 log \1 + 2*\/ 7 /| 2 log \1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 /
3*|pi + -----------------| pi + -----------------
\ 9 / 9
$$\left(\frac{\log{\left(8 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}} - \frac{i \pi \log{\left(8 \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}}\right) + \left(\left(\left(\frac{\log{\left(2 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{3 \left(\frac{\log{\left(1 + 2 \sqrt{7} \right)}^{2}}{9} + \pi^{2}\right)} - \frac{i \pi \log{\left(2 \right)}}{\frac{\log{\left(1 + 2 \sqrt{7} \right)}^{2}}{9} + \pi^{2}}\right) + \left(\left(\frac{\log{\left(8 \right)} \log{\left(-1 + 2 \sqrt{7} \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}} - \frac{2 i \pi \log{\left(8 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}}\right) + \left(\frac{3 \log{\left(2 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}} + \left(\frac{\log{\left(8 \right)} \log{\left(-1 + 2 \sqrt{7} \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}} + \frac{2 i \pi \log{\left(8 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}}\right)\right)\right)\right) + \left(\frac{\log{\left(8 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}} + \frac{i \pi \log{\left(8 \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}}\right)\right)$$
=
/ ___\ / ___\ / ___\
3*log(2) 2*log(8)*log\1 + 2*\/ 7 / 2*log(8)*log\-1 + 2*\/ 7 / log(2)*log\1 + 2*\/ 7 / pi*I*log(2)
----------------- + ------------------------- + -------------------------- + --------------------------- - -----------------------
/ ___\ 2 2/ ___\ 2/ ___\ 2 / 2/ ___\\ 2/ ___\
log\-1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 / log \-1 + 2*\/ 7 / + 4*pi | 2 log \1 + 2*\/ 7 /| 2 log \1 + 2*\/ 7 /
3*|pi + -----------------| pi + -----------------
\ 9 / 9
$$\frac{\log{\left(2 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{3 \left(\frac{\log{\left(1 + 2 \sqrt{7} \right)}^{2}}{9} + \pi^{2}\right)} + \frac{2 \log{\left(8 \right)} \log{\left(-1 + 2 \sqrt{7} \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}} + \frac{2 \log{\left(8 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}} + \frac{3 \log{\left(2 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}} - \frac{i \pi \log{\left(2 \right)}}{\frac{\log{\left(1 + 2 \sqrt{7} \right)}^{2}}{9} + \pi^{2}}$$
producto
/ / ___\ \ / / ___\ \ / / ___\ \ / / ___\ \ / / ___\ \
3*log(2) | log(8)*log\-1 + 2*\/ 7 / 2*pi*I*log(8) | | log(8)*log\-1 + 2*\/ 7 / 2*pi*I*log(8) | | log(2)*log\1 + 2*\/ 7 / pi*I*log(2) | |log(8)*log\1 + 2*\/ 7 / pi*I*log(8) | |log(8)*log\1 + 2*\/ 7 / pi*I*log(8) |
-----------------*|-------------------------- + --------------------------|*|-------------------------- - --------------------------|*|--------------------------- - -----------------------|*|----------------------- + -----------------------|*|----------------------- - -----------------------|
/ ___\ | 2/ ___\ 2 2/ ___\ 2| | 2/ ___\ 2 2/ ___\ 2| | / 2/ ___\\ 2/ ___\| | 2 2/ ___\ 2 2/ ___\| | 2 2/ ___\ 2 2/ ___\|
log\-1 + 2*\/ 7 / \log \-1 + 2*\/ 7 / + 4*pi log \-1 + 2*\/ 7 / + 4*pi / \log \-1 + 2*\/ 7 / + 4*pi log \-1 + 2*\/ 7 / + 4*pi / | | 2 log \1 + 2*\/ 7 /| 2 log \1 + 2*\/ 7 /| \pi + log \1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 // \pi + log \1 + 2*\/ 7 / pi + log \1 + 2*\/ 7 //
|3*|pi + -----------------| pi + -----------------|
\ \ 9 / 9 /
$$\frac{3 \log{\left(2 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}} \left(\frac{\log{\left(8 \right)} \log{\left(-1 + 2 \sqrt{7} \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}} + \frac{2 i \pi \log{\left(8 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}}\right) \left(\frac{\log{\left(8 \right)} \log{\left(-1 + 2 \sqrt{7} \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}} - \frac{2 i \pi \log{\left(8 \right)}}{\log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 4 \pi^{2}}\right) \left(\frac{\log{\left(2 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{3 \left(\frac{\log{\left(1 + 2 \sqrt{7} \right)}^{2}}{9} + \pi^{2}\right)} - \frac{i \pi \log{\left(2 \right)}}{\frac{\log{\left(1 + 2 \sqrt{7} \right)}^{2}}{9} + \pi^{2}}\right) \left(\frac{\log{\left(8 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}} + \frac{i \pi \log{\left(8 \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}}\right) \left(\frac{\log{\left(8 \right)} \log{\left(1 + 2 \sqrt{7} \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}} - \frac{i \pi \log{\left(8 \right)}}{\log{\left(1 + 2 \sqrt{7} \right)}^{2} + \pi^{2}}\right)$$
=
6 / / ___\ \
log (2)*\729*log\1 + 2*\/ 7 / - 2187*pi*I/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 6 4/ ___\ 2/ ___\ 2 4/ ___\ 4 2/ ___\ 4 2/ ___\ 2 2/ ___\ 2/ ___\\ / ___\
\36*pi + log \1 + 2*\/ 7 /*log \-1 + 2*\/ 7 / + 4*pi *log \1 + 2*\/ 7 / + 9*pi *log \-1 + 2*\/ 7 / + 40*pi *log \1 + 2*\/ 7 / + 10*pi *log \1 + 2*\/ 7 /*log \-1 + 2*\/ 7 //*log\-1 + 2*\/ 7 /
$$\frac{\left(729 \log{\left(1 + 2 \sqrt{7} \right)} - 2187 i \pi\right) \log{\left(2 \right)}^{6}}{\left(\log{\left(-1 + 2 \sqrt{7} \right)}^{2} \log{\left(1 + 2 \sqrt{7} \right)}^{4} + 4 \pi^{2} \log{\left(1 + 2 \sqrt{7} \right)}^{4} + 10 \pi^{2} \log{\left(-1 + 2 \sqrt{7} \right)}^{2} \log{\left(1 + 2 \sqrt{7} \right)}^{2} + 9 \pi^{4} \log{\left(-1 + 2 \sqrt{7} \right)}^{2} + 40 \pi^{4} \log{\left(1 + 2 \sqrt{7} \right)}^{2} + 36 \pi^{6}\right) \log{\left(-1 + 2 \sqrt{7} \right)}}$$
log(2)^6*(729*log(1 + 2*sqrt(7)) - 2187*pi*i)/((36*pi^6 + log(1 + 2*sqrt(7))^4*log(-1 + 2*sqrt(7))^2 + 4*pi^2*log(1 + 2*sqrt(7))^4 + 9*pi^4*log(-1 + 2*sqrt(7))^2 + 40*pi^4*log(1 + 2*sqrt(7))^2 + 10*pi^2*log(1 + 2*sqrt(7))^2*log(-1 + 2*sqrt(7))^2)*log(-1 + 2*sqrt(7)))
Respuesta numérica
[src]
x1 = 0.072811926678445 + 0.314073340770168*i
x2 = 0.072811926678445 - 0.314073340770168*i
x3 = 0.0414764801907947 - 0.212541665218781*i
x4 = 0.288592927895197 + 0.492954249276132*i
x5 = 0.288592927895197 - 0.492954249276132*i
x6 = 1.42756337856848
x6 = 1.42756337856848