Sr Examen

Otras calculadoras

((3^(2(x^2)-29)-27)*sqrt((5x+18),4))=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
/    2          \                 
| 2*x  - 29     |   __________    
\3          - 27/*\/ 5*x + 18  = 0
(32x2−29−27)5x+18=0\left(3^{2 x^{2} - 29} - 27\right) \sqrt{5 x + 18} = 0
Simplificar
Gráfica
-20.0-17.5-15.0-12.5-10.0-7.5-5.0-2.50.02.501
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = -4
x1=−4x_{1} = -4 
x2 = -18/5
x2=−185x_{2} = - \frac{18}{5} 
x3 = 4
x3=4x_{3} = 4 
                                    /    /      pi     \\                                  /    /      pi     \\
          ______________________    |atan|-------------||        ______________________    |atan|-------------||
       4 /   2      2               |    \log(43046721)/|     4 /   2      2               |    \log(43046721)/|
       \/  pi  + log (43046721) *cos|-------------------|   I*\/  pi  + log (43046721) *sin|-------------------|
                                    \         2         /                                  \         2         /
x4 = - -------------------------------------------------- - ----------------------------------------------------
                             ________                                              ________                     
                           \/ log(3)                                             \/ log(3)
x4=−π2+log⁡(43046721)24cos⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)−iπ2+log⁡(43046721)24sin⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)x_{4} = - \frac{\sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}} - \frac{i \sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}} 
                                  /    /      pi     \\                                  /    /      pi     \\
        ______________________    |atan|-------------||        ______________________    |atan|-------------||
     4 /   2      2               |    \log(43046721)/|     4 /   2      2               |    \log(43046721)/|
     \/  pi  + log (43046721) *cos|-------------------|   I*\/  pi  + log (43046721) *sin|-------------------|
                                  \         2         /                                  \         2         /
x5 = -------------------------------------------------- + ----------------------------------------------------
                           ________                                              ________                     
                         \/ log(3)                                             \/ log(3)
x5=π2+log⁡(43046721)24cos⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)+iπ2+log⁡(43046721)24sin⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)x_{5} = \frac{\sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}} + \frac{i \sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}} 
x5 = (pi^2 + log(43046721)^2)^(1/4)*cos(atan(pi/log(43046721))/2)/sqrt(log(3)) + i*(pi^2 + log(43046721)^2)^(1/4)*sin(atan(pi/log(43046721))/2)/sqrt(log(3))
Suma y producto de raíces [src] 
suma
                                               /    /      pi     \\                                  /    /      pi     \\                                /    /      pi     \\                                  /    /      pi     \\
                     ______________________    |atan|-------------||        ______________________    |atan|-------------||      ______________________    |atan|-------------||        ______________________    |atan|-------------||
                  4 /   2      2               |    \log(43046721)/|     4 /   2      2               |    \log(43046721)/|   4 /   2      2               |    \log(43046721)/|     4 /   2      2               |    \log(43046721)/|
                  \/  pi  + log (43046721) *cos|-------------------|   I*\/  pi  + log (43046721) *sin|-------------------|   \/  pi  + log (43046721) *cos|-------------------|   I*\/  pi  + log (43046721) *sin|-------------------|
                                               \         2         /                                  \         2         /                                \         2         /                                  \         2         /
-4 - 18/5 + 4 + - -------------------------------------------------- - ---------------------------------------------------- + -------------------------------------------------- + ----------------------------------------------------
                                        ________                                              ________                                              ________                                              ________                     
                                      \/ log(3)                                             \/ log(3)                                             \/ log(3)                                             \/ log(3)
(((−4−185)+4)+(−π2+log⁡(43046721)24cos⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)−iπ2+log⁡(43046721)24sin⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)))+(π2+log⁡(43046721)24cos⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)+iπ2+log⁡(43046721)24sin⁡(atan⁡(πlog⁡(43046721))2)log⁡(3))\left(\left(\left(-4 - \frac{18}{5}\right) + 4\right) + \left(- \frac{\sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}} - \frac{i \sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}}\right)\right) + \left(\frac{\sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}} + \frac{i \sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}}\right) 
=
-18/5
−185- \frac{18}{5} 
producto
           /                               /    /      pi     \\                                  /    /      pi     \\\ /                             /    /      pi     \\                                  /    /      pi     \\\
           |     ______________________    |atan|-------------||        ______________________    |atan|-------------||| |   ______________________    |atan|-------------||        ______________________    |atan|-------------|||
           |  4 /   2      2               |    \log(43046721)/|     4 /   2      2               |    \log(43046721)/|| |4 /   2      2               |    \log(43046721)/|     4 /   2      2               |    \log(43046721)/||
           |  \/  pi  + log (43046721) *cos|-------------------|   I*\/  pi  + log (43046721) *sin|-------------------|| |\/  pi  + log (43046721) *cos|-------------------|   I*\/  pi  + log (43046721) *sin|-------------------||
-4*(-18)   |                               \         2         /                                  \         2         /| |                             \         2         /                                  \         2         /|
--------*4*|- -------------------------------------------------- - ----------------------------------------------------|*|-------------------------------------------------- + ----------------------------------------------------|
   5       |                        ________                                              ________                     | |                      ________                                              ________                     |
           \                      \/ log(3)                                             \/ log(3)                      / \                    \/ log(3)                                             \/ log(3)                      /
4(−−725)(−π2+log⁡(43046721)24cos⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)−iπ2+log⁡(43046721)24sin⁡(atan⁡(πlog⁡(43046721))2)log⁡(3))(π2+log⁡(43046721)24cos⁡(atan⁡(πlog⁡(43046721))2)log⁡(3)+iπ2+log⁡(43046721)24sin⁡(atan⁡(πlog⁡(43046721))2)log⁡(3))4 \left(- \frac{-72}{5}\right) \left(- \frac{\sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}} - \frac{i \sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}}\right) \left(\frac{\sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}} + \frac{i \sqrt[4]{\pi^{2} + \log{\left(43046721 \right)}^{2}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}{2} \right)}}{\sqrt{\log{\left(3 \right)}}}\right) 
=
                                      /      pi     \
        ______________________  I*atan|-------------|
       /   2      2                   \log(43046721)/
-288*\/  pi  + log (43046721) *e                     
-----------------------------------------------------
                       5*log(3)
−288π2+log⁡(43046721)2eiatan⁡(πlog⁡(43046721))5log⁡(3)- \frac{288 \sqrt{\pi^{2} + \log{\left(43046721 \right)}^{2}} e^{i \operatorname{atan}{\left(\frac{\pi}{\log{\left(43046721 \right)}} \right)}}}{5 \log{\left(3 \right)}} 
-288*sqrt(pi^2 + log(43046721)^2)*exp(i*atan(pi/log(43046721)))/(5*log(3))
Respuesta numérica [src] 
x1 = -4.0
x2 = -3.6
x3 = 4.0
x4 = -4.01581451579495 - 0.356042448690394*i
x5 = 4.01581451579495 + 0.356042448690394*i
x5 = 4.01581451579495 + 0.356042448690394*i
    © Sr Examen – Калькулятор