Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación (x+9)^2=36*x
-
Ecuación a+120=2000/5
-
Ecuación -x/11+x=50/11
-
Ecuación x^2+7x+6=0
- Expresar {x} en función de y en la ecuación:
- 12*x+8*y=18
- 8*x+6*y=20
- -2*x+18*y=13
- -11*x-1*y=15
-
Expresiones idénticas
- (x^ dos +5x)^ dos - dos (x+5x)- veinticuatro = cero
- (x al cuadrado más 5x) al cuadrado menos 2(x más 5x) menos 24 es igual a 0
- (x en el grado dos más 5x) en el grado dos menos dos (x más 5x) menos veinticuatro es igual a cero
- (x2+5x)2-2(x+5x)-24=0
- x2+5x2-2x+5x-24=0
- (x²+5x)²-2(x+5x)-24=0
- (x en el grado 2+5x) en el grado 2-2(x+5x)-24=0
- x^2+5x^2-2x+5x-24=0
- (x^2+5x)^2-2(x+5x)-24=O
-
Expresiones semejantes
- (x^2+5x)^2-2(x+5x)+24=0
- (x^2+5x)^2-2(x-5x)-24=0
- (x^2+5x)^2+2(x+5x)-24=0
- (x^2-5x)^2-2(x+5x)-24=0
(x^2+5x)^2-2(x+5x)-24=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 / 2 \ \x + 5*x/ - 2*(x + 5*x) - 24 = 0
$$\left(- 2 \left(x + 5 x\right) + \left(x^{2} + 5 x\right)^{2}\right) - 24 = 0$$
Suma y producto de raíces
[src]
suma
________________ / ________________ \ ________________ / ________________ \
/ ____ | / ____ | / ____ | / ____ |
/ 127 2*\/ 43 | ___ / 127 2*\/ 43 | / 127 2*\/ 43 | ___ / 127 2*\/ 43 | ________________
3 / --- + -------- | \/ 3 *3 / --- + -------- ___ | 3 / --- + -------- |\/ 3 *3 / --- + -------- ___ | / ____
11 13 \/ 27 3 | \/ 27 3 13*\/ 3 | 11 13 \/ 27 3 | \/ 27 3 13*\/ 3 | 11 / 127 2*\/ 43 13
1 + - -- - ------------------------ - --------------------- + I*|- --------------------------- + ------------------------| + - -- - ------------------------ - --------------------- + I*|--------------------------- - ------------------------| + - -- + 3 / --- + -------- + -----------------------
3 ________________ 2 | 2 ________________| 3 ________________ 2 | 2 ________________| 3 \/ 27 3 ________________
/ ____ | / ____ | / ____ | / ____ | / ____
/ 127 2*\/ 43 | / 127 2*\/ 43 | / 127 2*\/ 43 | / 127 2*\/ 43 | / 127 2*\/ 43
18*3 / --- + -------- | 18*3 / --- + -------- | 18*3 / --- + -------- | 18*3 / --- + -------- | 9*3 / --- + --------
\/ 27 3 \ \/ 27 3 / \/ 27 3 \ \/ 27 3 / \/ 27 3
$$\left(- \frac{11}{3} + \frac{13}{9 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}\right) + \left(\left(1 + \left(- \frac{11}{3} - \frac{\sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} - \frac{13}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} + \frac{13 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}\right)\right)\right) + \left(- \frac{11}{3} - \frac{\sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} - \frac{13}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + i \left(- \frac{13 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2}\right)\right)\right)$$
=
/ ________________ \ / ________________ \
| / ____ | | / ____ |
| ___ / 127 2*\/ 43 | | ___ / 127 2*\/ 43 |
|\/ 3 *3 / --- + -------- ___ | | \/ 3 *3 / --- + -------- ___ |
| \/ 27 3 13*\/ 3 | | \/ 27 3 13*\/ 3 |
-10 + I*|--------------------------- - ------------------------| + I*|- --------------------------- + ------------------------|
| 2 ________________| | 2 ________________|
| / ____ | | / ____ |
| / 127 2*\/ 43 | | / 127 2*\/ 43 |
| 18*3 / --- + -------- | | 18*3 / --- + -------- |
\ \/ 27 3 / \ \/ 27 3 /
$$-10 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} + \frac{13 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}\right) + i \left(- \frac{13 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2}\right)$$
producto
/ ________________ / ________________ \\ / ________________ / ________________ \\ | / ____ | / ____ || | / ____ | / ____ || | / 127 2*\/ 43 | ___ / 127 2*\/ 43 || | / 127 2*\/ 43 | ___ / 127 2*\/ 43 || / ________________ \ | 3 / --- + -------- | \/ 3 *3 / --- + -------- ___ || | 3 / --- + -------- |\/ 3 *3 / --- + -------- ___ || | / ____ | | 11 13 \/ 27 3 | \/ 27 3 13*\/ 3 || | 11 13 \/ 27 3 | \/ 27 3 13*\/ 3 || | 11 / 127 2*\/ 43 13 | |- -- - ------------------------ - --------------------- + I*|- --------------------------- + ------------------------||*|- -- - ------------------------ - --------------------- + I*|--------------------------- - ------------------------||*|- -- + 3 / --- + -------- + -----------------------| | 3 ________________ 2 | 2 ________________|| | 3 ________________ 2 | 2 ________________|| | 3 \/ 27 3 ________________| | / ____ | / ____ || | / ____ | / ____ || | / ____ | | / 127 2*\/ 43 | / 127 2*\/ 43 || | / 127 2*\/ 43 | / 127 2*\/ 43 || | / 127 2*\/ 43 | | 18*3 / --- + -------- | 18*3 / --- + -------- || | 18*3 / --- + -------- | 18*3 / --- + -------- || | 9*3 / --- + -------- | \ \/ 27 3 \ \/ 27 3 // \ \/ 27 3 \ \/ 27 3 // \ \/ 27 3 /
$$\left(- \frac{11}{3} - \frac{\sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} - \frac{13}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + i \left(- \frac{13 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2}\right)\right) \left(- \frac{11}{3} - \frac{\sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} - \frac{13}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} + \frac{13 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}\right)\right) \left(- \frac{11}{3} + \frac{13}{9 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}\right)$$
=
-24
$$-24$$
-24
Respuesta rápida
[src]
x1 = 1
$$x_{1} = 1$$
________________ / ________________ \
/ ____ | / ____ |
/ 127 2*\/ 43 | ___ / 127 2*\/ 43 |
3 / --- + -------- | \/ 3 *3 / --- + -------- ___ |
11 13 \/ 27 3 | \/ 27 3 13*\/ 3 |
x2 = - -- - ------------------------ - --------------------- + I*|- --------------------------- + ------------------------|
3 ________________ 2 | 2 ________________|
/ ____ | / ____ |
/ 127 2*\/ 43 | / 127 2*\/ 43 |
18*3 / --- + -------- | 18*3 / --- + -------- |
\/ 27 3 \ \/ 27 3 /
$$x_{2} = - \frac{11}{3} - \frac{\sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} - \frac{13}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} + \frac{13 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}\right)$$
________________ / ________________ \
/ ____ | / ____ |
/ 127 2*\/ 43 | ___ / 127 2*\/ 43 |
3 / --- + -------- |\/ 3 *3 / --- + -------- ___ |
11 13 \/ 27 3 | \/ 27 3 13*\/ 3 |
x3 = - -- - ------------------------ - --------------------- + I*|--------------------------- - ------------------------|
3 ________________ 2 | 2 ________________|
/ ____ | / ____ |
/ 127 2*\/ 43 | / 127 2*\/ 43 |
18*3 / --- + -------- | 18*3 / --- + -------- |
\/ 27 3 \ \/ 27 3 /
$$x_{3} = - \frac{11}{3} - \frac{\sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2} - \frac{13}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + i \left(- \frac{13 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}}{2}\right)$$
________________
/ ____
11 / 127 2*\/ 43 13
x4 = - -- + 3 / --- + -------- + -----------------------
3 \/ 27 3 ________________
/ ____
/ 127 2*\/ 43
9*3 / --- + --------
\/ 27 3
$$x_{4} = - \frac{11}{3} + \frac{13}{9 \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}} + \sqrt[3]{\frac{2 \sqrt{43}}{3} + \frac{127}{27}}$$
x4 = -11/3 + 13/(9*(2*sqrt(43)/3 + 127/27)^(1/3)) + (2*sqrt(43)/3 + 127/27)^(1/3)
Respuesta numérica
[src]
x1 = -0.888305779071753
x2 = 1.0
x3 = -5.05584711046412 + 1.20670360194812*i
x4 = -5.05584711046412 - 1.20670360194812*i
x4 = -5.05584711046412 - 1.20670360194812*i