Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación (x-3)*(x+2)=0
-
Ecuación z^2-6*z+10=0
-
Ecuación 4/(x-4)=-5
-
Ecuación (x-6)^2=-24*x
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- -14*x-12*y=5
-
Expresiones idénticas
- -1 dos cero x^2+12sqrt(seis)*x+8 cuatro sqrt(seis)x^ tres -144x^4=0
- menos 120x al cuadrado más 12 raíz cuadrada de (6) multiplicar por x más 84 raíz cuadrada de (6)x al cubo menos 144x en el grado 4 es igual a 0
- menos 1 dos cero x al cuadrado más 12 raíz cuadrada de (seis) multiplicar por x más 8 cuatro raíz cuadrada de (seis)x en el grado tres menos 144x en el grado 4 es igual a 0
- -120x^2+12√(6)*x+84√(6)x^3-144x^4=0
- -120x2+12sqrt(6)*x+84sqrt(6)x3-144x4=0
- -120x2+12sqrt6*x+84sqrt6x3-144x4=0
- -120x²+12sqrt(6)*x+84sqrt(6)x³-144x⁴=0
- -120x en el grado 2+12sqrt(6)*x+84sqrt(6)x en el grado 3-144x en el grado 4=0
- -120x^2+12sqrt(6)x+84sqrt(6)x^3-144x^4=0
- -120x2+12sqrt(6)x+84sqrt(6)x3-144x4=0
- -120x2+12sqrt6x+84sqrt6x3-144x4=0
- -120x^2+12sqrt6x+84sqrt6x^3-144x^4=0
- -120x^2+12sqrt(6)*x+84sqrt(6)x^3-144x^4=O
-
Expresiones semejantes
- 120x^2+12sqrt(6)*x+84sqrt(6)x^3-144x^4=0
- -120x^2+12sqrt(6)*x+84sqrt(6)x^3+144x^4=0
- -120x^2+12sqrt(6)*x-84sqrt(6)x^3-144x^4=0
- -120x^2-12sqrt(6)*x+84sqrt(6)x^3-144x^4=0
-120x^2+12sqrt(6)*x+84sqrt(6)x^3-144x^4=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 ___ ___ 3 4 - 120*x + 12*\/ 6 *x + 84*\/ 6 *x - 144*x = 0
$$- 144 x^{4} + \left(84 \sqrt{6} x^{3} + \left(- 120 x^{2} + 12 \sqrt{6} x\right)\right) = 0$$
Suma y producto de raíces
[src]
suma
____________________ / ____________________\ ____________________ / ____________________ \
/ ___ ___ | / ___ ___ | / ___ ___ | / ___ ___ |
/ 5*\/ 2 37*\/ 6 | ___ / 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6 | ___ / 5*\/ 2 37*\/ 6 | ____________________
3 / ------- + -------- ___ | ___ \/ 3 *3 / ------- + -------- | 3 / ------- + -------- ___ |\/ 3 *3 / ------- + -------- ___ | / ___ ___ ___
\/ 432 7776 7*\/ 6 11 | 11*\/ 3 \/ 432 7776 | \/ 432 7776 7*\/ 6 11 | \/ 432 7776 11*\/ 3 | / 5*\/ 2 37*\/ 6 11 7*\/ 6
- ------------------------- + ------- + ----------------------------- + I*|- ----------------------------- - -------------------------------| + - ------------------------- + ------- + ----------------------------- + I*|------------------------------- + -----------------------------| + 3 / ------- + -------- - ----------------------------- + -------
2 36 ____________________ | ____________________ 2 | 2 36 ____________________ | 2 ____________________| \/ 432 7776 ____________________ 36
/ ___ ___ | / ___ ___ | / ___ ___ | / ___ ___ | / ___ ___
/ 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6
432*3 / ------- + -------- | 432*3 / ------- + -------- | 432*3 / ------- + -------- | 432*3 / ------- + -------- | 216*3 / ------- + --------
\/ 432 7776 \ \/ 432 7776 / \/ 432 7776 \ \/ 432 7776 / \/ 432 7776
$$\left(- \frac{11}{216 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}} + \frac{7 \sqrt{6}}{36}\right) + \left(\left(- \frac{\sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} + \frac{11}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{7 \sqrt{6}}{36} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} - \frac{11 \sqrt{3}}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} + \frac{11}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{7 \sqrt{6}}{36} + i \left(\frac{11 \sqrt{3}}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{\sqrt{3} \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2}\right)\right)\right)$$
=
/ ____________________ \ / ____________________\
| / ___ ___ | | / ___ ___ |
| ___ / 5*\/ 2 37*\/ 6 | | ___ / 5*\/ 2 37*\/ 6 |
___ |\/ 3 *3 / ------- + -------- ___ | | ___ \/ 3 *3 / ------- + -------- |
7*\/ 6 | \/ 432 7776 11*\/ 3 | | 11*\/ 3 \/ 432 7776 |
------- + I*|------------------------------- + -----------------------------| + I*|- ----------------------------- - -------------------------------|
12 | 2 ____________________| | ____________________ 2 |
| / ___ ___ | | / ___ ___ |
| / 5*\/ 2 37*\/ 6 | | / 5*\/ 2 37*\/ 6 |
| 432*3 / ------- + -------- | | 432*3 / ------- + -------- |
\ \/ 432 7776 / \ \/ 432 7776 /
$$\frac{7 \sqrt{6}}{12} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} - \frac{11 \sqrt{3}}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}\right) + i \left(\frac{11 \sqrt{3}}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{\sqrt{3} \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2}\right)$$
producto
/ ____________________ / ____________________\\ / ____________________ / ____________________ \\ | / ___ ___ | / ___ ___ || | / ___ ___ | / ___ ___ || | / 5*\/ 2 37*\/ 6 | ___ / 5*\/ 2 37*\/ 6 || | / 5*\/ 2 37*\/ 6 | ___ / 5*\/ 2 37*\/ 6 || / ____________________ \ | 3 / ------- + -------- ___ | ___ \/ 3 *3 / ------- + -------- || | 3 / ------- + -------- ___ |\/ 3 *3 / ------- + -------- ___ || | / ___ ___ ___| | \/ 432 7776 7*\/ 6 11 | 11*\/ 3 \/ 432 7776 || | \/ 432 7776 7*\/ 6 11 | \/ 432 7776 11*\/ 3 || | / 5*\/ 2 37*\/ 6 11 7*\/ 6 | 0*|- ------------------------- + ------- + ----------------------------- + I*|- ----------------------------- - -------------------------------||*|- ------------------------- + ------- + ----------------------------- + I*|------------------------------- + -----------------------------||*|3 / ------- + -------- - ----------------------------- + -------| | 2 36 ____________________ | ____________________ 2 || | 2 36 ____________________ | 2 ____________________|| |\/ 432 7776 ____________________ 36 | | / ___ ___ | / ___ ___ || | / ___ ___ | / ___ ___ || | / ___ ___ | | / 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6 || | / 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6 || | / 5*\/ 2 37*\/ 6 | | 432*3 / ------- + -------- | 432*3 / ------- + -------- || | 432*3 / ------- + -------- | 432*3 / ------- + -------- || | 216*3 / ------- + -------- | \ \/ 432 7776 \ \/ 432 7776 // \ \/ 432 7776 \ \/ 432 7776 // \ \/ 432 7776 /
$$\left(- \frac{\sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} + \frac{11}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{7 \sqrt{6}}{36} + i \left(\frac{11 \sqrt{3}}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{\sqrt{3} \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2}\right)\right) 0 \left(- \frac{\sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} + \frac{11}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{7 \sqrt{6}}{36} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} - \frac{11 \sqrt{3}}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}\right)\right) \left(- \frac{11}{216 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}} + \frac{7 \sqrt{6}}{36}\right)$$
=
0
$$0$$
0
Respuesta rápida
[src]
x1 = 0
$$x_{1} = 0$$
____________________ / ____________________\
/ ___ ___ | / ___ ___ |
/ 5*\/ 2 37*\/ 6 | ___ / 5*\/ 2 37*\/ 6 |
3 / ------- + -------- ___ | ___ \/ 3 *3 / ------- + -------- |
\/ 432 7776 7*\/ 6 11 | 11*\/ 3 \/ 432 7776 |
x2 = - ------------------------- + ------- + ----------------------------- + I*|- ----------------------------- - -------------------------------|
2 36 ____________________ | ____________________ 2 |
/ ___ ___ | / ___ ___ |
/ 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6 |
432*3 / ------- + -------- | 432*3 / ------- + -------- |
\/ 432 7776 \ \/ 432 7776 /
$$x_{2} = - \frac{\sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} + \frac{11}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{7 \sqrt{6}}{36} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} - \frac{11 \sqrt{3}}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}\right)$$
____________________ / ____________________ \
/ ___ ___ | / ___ ___ |
/ 5*\/ 2 37*\/ 6 | ___ / 5*\/ 2 37*\/ 6 |
3 / ------- + -------- ___ |\/ 3 *3 / ------- + -------- ___ |
\/ 432 7776 7*\/ 6 11 | \/ 432 7776 11*\/ 3 |
x3 = - ------------------------- + ------- + ----------------------------- + I*|------------------------------- + -----------------------------|
2 36 ____________________ | 2 ____________________|
/ ___ ___ | / ___ ___ |
/ 5*\/ 2 37*\/ 6 | / 5*\/ 2 37*\/ 6 |
432*3 / ------- + -------- | 432*3 / ------- + -------- |
\/ 432 7776 \ \/ 432 7776 /
$$x_{3} = - \frac{\sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2} + \frac{11}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{7 \sqrt{6}}{36} + i \left(\frac{11 \sqrt{3}}{432 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \frac{\sqrt{3} \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}}{2}\right)$$
____________________
/ ___ ___ ___
/ 5*\/ 2 37*\/ 6 11 7*\/ 6
x4 = 3 / ------- + -------- - ----------------------------- + -------
\/ 432 7776 ____________________ 36
/ ___ ___
/ 5*\/ 2 37*\/ 6
216*3 / ------- + --------
\/ 432 7776
$$x_{4} = - \frac{11}{216 \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}}} + \sqrt[3]{\frac{37 \sqrt{6}}{7776} + \frac{5 \sqrt{2}}{432}} + \frac{7 \sqrt{6}}{36}$$
x4 = -11/(216*(37*sqrt(6)/7776 + 5*sqrt(2)/432)^(1/3)) + (37*sqrt(6)/7776 + 5*sqrt(2)/432)^(1/3) + 7*sqrt(6)/36
Respuesta numérica
[src]
x1 = 0.0
x2 = 0.408248290463863 + 0.408248290463863*i
x3 = 0.612372435695794
x4 = 0.408248290463863 - 0.408248290463863*i
x4 = 0.408248290463863 - 0.408248290463863*i