Sr Examen

Otras calculadoras

x^3-4*x^2+9x+36=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] 
 3      2               
x  - 4*x  + 9*x + 36 = 0
(9x+(x3−4x2))+36=0\left(9 x + \left(x^{3} - 4 x^{2}\right)\right) + 36 = 0
Simplificar
Teorema de Cardano-Vieta
es ecuación cúbica reducida
px2+qx+v+x3=0p x^{2} + q x + v + x^{3} = 0
donde
p=bap = \frac{b}{a}
p=−4p = -4
q=caq = \frac{c}{a}
q=9q = 9
v=dav = \frac{d}{a}
v=36v = 36
Fórmulas de Cardano-Vieta
x1+x2+x3=−px_{1} + x_{2} + x_{3} = - p
x1x2+x1x3+x2x3=qx_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q
x1x2x3=vx_{1} x_{2} x_{3} = v
x1+x2+x3=4x_{1} + x_{2} + x_{3} = 4
x1x2+x1x3+x2x3=9x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 9
x1x2x3=36x_{1} x_{2} x_{3} = 36
Gráfica
-17.5-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.0-25002500
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
                                      __________________     /         __________________                          \
                                   3 /           ______      |  ___ 3 /           ______                 ___       |
     4              11             \/  584 + 9*\/ 4227       |\/ 3 *\/  584 + 9*\/ 4227             11*\/ 3        |
x1 = - - ----------------------- + --------------------- + I*|--------------------------- + -----------------------|
     3        __________________             6               |             6                     __________________|
           3 /           ______                              |                                3 /           ______ |
         6*\/  584 + 9*\/ 4227                               \                              6*\/  584 + 9*\/ 4227  /
x1=−116584+942273+43+584+9422736+i(1136584+942273+3584+9422736)x_{1} = - \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(\frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6}\right) 
                                      __________________     /                                     __________________\
                                   3 /           ______      |               ___            ___ 3 /           ______ |
     4              11             \/  584 + 9*\/ 4227       |          11*\/ 3           \/ 3 *\/  584 + 9*\/ 4227  |
x2 = - - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------|
     3        __________________             6               |       __________________                6             |
           3 /           ______                              |    3 /           ______                               |
         6*\/  584 + 9*\/ 4227                               \  6*\/  584 + 9*\/ 4227                                /
x2=−116584+942273+43+584+9422736+i(−3584+9422736−1136584+942273)x_{2} = - \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6} - \frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}}\right) 
            __________________                          
         3 /           ______                           
     4   \/  584 + 9*\/ 4227                11          
x3 = - - --------------------- + -----------------------
     3             3                  __________________
                                   3 /           ______ 
                                 3*\/  584 + 9*\/ 4227
x3=−584+9422733+113584+942273+43x_{3} = - \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{3} + \frac{11}{3 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} 
x3 = -(584 + 9*sqrt(4227))^(1/3)/3 + 11/(3*(584 + 9*sqrt(4227))^(1/3)) + 4/3
Suma y producto de raíces [src] 
suma
                                 __________________     /         __________________                          \                                    __________________     /                                     __________________\          __________________                          
                              3 /           ______      |  ___ 3 /           ______                 ___       |                                 3 /           ______      |               ___            ___ 3 /           ______ |       3 /           ______                           
4              11             \/  584 + 9*\/ 4227       |\/ 3 *\/  584 + 9*\/ 4227             11*\/ 3        |   4              11             \/  584 + 9*\/ 4227       |          11*\/ 3           \/ 3 *\/  584 + 9*\/ 4227  |   4   \/  584 + 9*\/ 4227                11          
- - ----------------------- + --------------------- + I*|--------------------------- + -----------------------| + - - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------| + - - --------------------- + -----------------------
3        __________________             6               |             6                     __________________|   3        __________________             6               |       __________________                6             |   3             3                  __________________
      3 /           ______                              |                                3 /           ______ |         3 /           ______                              |    3 /           ______                               |                                 3 /           ______ 
    6*\/  584 + 9*\/ 4227                               \                              6*\/  584 + 9*\/ 4227  /       6*\/  584 + 9*\/ 4227                               \  6*\/  584 + 9*\/ 4227                                /                               3*\/  584 + 9*\/ 4227
(−584+9422733+113584+942273+43)+((−116584+942273+43+584+9422736+i(−3584+9422736−1136584+942273))+(−116584+942273+43+584+9422736+i(1136584+942273+3584+9422736)))\left(- \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{3} + \frac{11}{3 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3}\right) + \left(\left(- \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6} - \frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}}\right)\right) + \left(- \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(\frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6}\right)\right)\right) 
=
      /                                     __________________\     /         __________________                          \
      |               ___            ___ 3 /           ______ |     |  ___ 3 /           ______                 ___       |
      |          11*\/ 3           \/ 3 *\/  584 + 9*\/ 4227  |     |\/ 3 *\/  584 + 9*\/ 4227             11*\/ 3        |
4 + I*|- ----------------------- - ---------------------------| + I*|--------------------------- + -----------------------|
      |       __________________                6             |     |             6                     __________________|
      |    3 /           ______                               |     |                                3 /           ______ |
      \  6*\/  584 + 9*\/ 4227                                /     \                              6*\/  584 + 9*\/ 4227  /
4+i(−3584+9422736−1136584+942273)+i(1136584+942273+3584+9422736)4 + i \left(- \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6} - \frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}}\right) + i \left(\frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6}\right) 
producto
/                                 __________________     /         __________________                          \\ /                                 __________________     /                                     __________________\\ /       __________________                          \
|                              3 /           ______      |  ___ 3 /           ______                 ___       || |                              3 /           ______      |               ___            ___ 3 /           ______ || |    3 /           ______                           |
|4              11             \/  584 + 9*\/ 4227       |\/ 3 *\/  584 + 9*\/ 4227             11*\/ 3        || |4              11             \/  584 + 9*\/ 4227       |          11*\/ 3           \/ 3 *\/  584 + 9*\/ 4227  || |4   \/  584 + 9*\/ 4227                11          |
|- - ----------------------- + --------------------- + I*|--------------------------- + -----------------------||*|- - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------||*|- - --------------------- + -----------------------|
|3        __________________             6               |             6                     __________________|| |3        __________________             6               |       __________________                6             || |3             3                  __________________|
|      3 /           ______                              |                                3 /           ______ || |      3 /           ______                              |    3 /           ______                               || |                              3 /           ______ |
\    6*\/  584 + 9*\/ 4227                               \                              6*\/  584 + 9*\/ 4227  // \    6*\/  584 + 9*\/ 4227                               \  6*\/  584 + 9*\/ 4227                                // \                            3*\/  584 + 9*\/ 4227  /
(−116584+942273+43+584+9422736+i(1136584+942273+3584+9422736))(−116584+942273+43+584+9422736+i(−3584+9422736−1136584+942273))(−584+9422733+113584+942273+43)\left(- \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(\frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6}\right)\right) \left(- \frac{11}{6 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3} + \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{584 + 9 \sqrt{4227}}}{6} - \frac{11 \sqrt{3}}{6 \sqrt[3]{584 + 9 \sqrt{4227}}}\right)\right) \left(- \frac{\sqrt[3]{584 + 9 \sqrt{4227}}}{3} + \frac{11}{3 \sqrt[3]{584 + 9 \sqrt{4227}}} + \frac{4}{3}\right) 
=
-36
−36-36 
-36
Respuesta numérica [src] 
x1 = -1.83017552053575
x2 = 2.91508776026788 + 3.34253015963173*i
x3 = 2.91508776026788 - 3.34253015963173*i
x3 = 2.91508776026788 - 3.34253015963173*i
    © Sr Examen – Калькулятор