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- La ecuación:
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Ecuación 5*x^2+2*x-7=0
-
Ecuación x+120=40*5
-
Ecuación y(0)=1
-
Ecuación x-2,4/6=x+0,6/11
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 16*x-11*y=13
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Expresiones idénticas
- (x- dos)*(x- cinco)*(x- cuatro)= cuatro
- (x menos 2) multiplicar por (x menos 5) multiplicar por (x menos 4) es igual a 4
- (x menos dos) multiplicar por (x menos cinco) multiplicar por (x menos cuatro) es igual a cuatro
- (x-2)(x-5)(x-4)=4
- x-2x-5x-4=4
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Expresiones semejantes
- (x-2)*(x+5)*(x-4)=4
- (x-2)*(x-5)*(x+4)=4
- (x+2)*(x-5)*(x-4)=4
(x-2)*(x-5)*(x-4)=4 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
(x - 2)*(x - 5)*(x - 4) = 4
$$\left(x - 5\right) \left(x - 2\right) \left(x - 4\right) = 4$$
Suma y producto de raíces
[src]
suma
______________ / ______________ \ ______________ / ______________ \
/ _____ | / _____ | / _____ | / _____ |
/ 44 \/ 177 | ___ / 44 \/ 177 | / 44 \/ 177 | ___ / 44 \/ 177 | ______________
3 / -- + ------- | \/ 3 *3 / -- + ------- ___ | 3 / -- + ------- |\/ 3 *3 / -- + ------- ___ | / _____
11 7 \/ 27 9 | \/ 27 9 7*\/ 3 | 11 7 \/ 27 9 | \/ 27 9 7*\/ 3 | 11 / 44 \/ 177 7
-- - ---------------------- - ------------------- + I*|- ------------------------- + ----------------------| + -- - ---------------------- - ------------------- + I*|------------------------- - ----------------------| + -- + 3 / -- + ------- + ---------------------
3 ______________ 2 | 2 ______________| 3 ______________ 2 | 2 ______________| 3 \/ 27 9 ______________
/ _____ | / _____ | / _____ | / _____ | / _____
/ 44 \/ 177 | / 44 \/ 177 | / 44 \/ 177 | / 44 \/ 177 | / 44 \/ 177
18*3 / -- + ------- | 18*3 / -- + ------- | 18*3 / -- + ------- | 18*3 / -- + ------- | 9*3 / -- + -------
\/ 27 9 \ \/ 27 9 / \/ 27 9 \ \/ 27 9 / \/ 27 9
$$\left(\frac{7}{9 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}} + \frac{11}{3}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} - \frac{7}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{11}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} + \frac{7 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} - \frac{7}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{11}{3} + i \left(- \frac{7 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2}\right)\right)\right)$$
=
/ ______________ \ / ______________ \
| / _____ | | / _____ |
| ___ / 44 \/ 177 | | ___ / 44 \/ 177 |
|\/ 3 *3 / -- + ------- ___ | | \/ 3 *3 / -- + ------- ___ |
| \/ 27 9 7*\/ 3 | | \/ 27 9 7*\/ 3 |
11 + I*|------------------------- - ----------------------| + I*|- ------------------------- + ----------------------|
| 2 ______________| | 2 ______________|
| / _____ | | / _____ |
| / 44 \/ 177 | | / 44 \/ 177 |
| 18*3 / -- + ------- | | 18*3 / -- + ------- |
\ \/ 27 9 / \ \/ 27 9 /
$$11 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} + \frac{7 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}\right) + i \left(- \frac{7 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2}\right)$$
producto
/ ______________ / ______________ \\ / ______________ / ______________ \\ | / _____ | / _____ || | / _____ | / _____ || | / 44 \/ 177 | ___ / 44 \/ 177 || | / 44 \/ 177 | ___ / 44 \/ 177 || / ______________ \ | 3 / -- + ------- | \/ 3 *3 / -- + ------- ___ || | 3 / -- + ------- |\/ 3 *3 / -- + ------- ___ || | / _____ | |11 7 \/ 27 9 | \/ 27 9 7*\/ 3 || |11 7 \/ 27 9 | \/ 27 9 7*\/ 3 || |11 / 44 \/ 177 7 | |-- - ---------------------- - ------------------- + I*|- ------------------------- + ----------------------||*|-- - ---------------------- - ------------------- + I*|------------------------- - ----------------------||*|-- + 3 / -- + ------- + ---------------------| |3 ______________ 2 | 2 ______________|| |3 ______________ 2 | 2 ______________|| |3 \/ 27 9 ______________| | / _____ | / _____ || | / _____ | / _____ || | / _____ | | / 44 \/ 177 | / 44 \/ 177 || | / 44 \/ 177 | / 44 \/ 177 || | / 44 \/ 177 | | 18*3 / -- + ------- | 18*3 / -- + ------- || | 18*3 / -- + ------- | 18*3 / -- + ------- || | 9*3 / -- + ------- | \ \/ 27 9 \ \/ 27 9 // \ \/ 27 9 \ \/ 27 9 // \ \/ 27 9 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} - \frac{7}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{11}{3} + i \left(- \frac{7 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} - \frac{7}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{11}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} + \frac{7 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}\right)\right) \left(\frac{7}{9 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}} + \frac{11}{3}\right)$$
=
44
$$44$$
44
Respuesta rápida
[src]
______________ / ______________ \
/ _____ | / _____ |
/ 44 \/ 177 | ___ / 44 \/ 177 |
3 / -- + ------- | \/ 3 *3 / -- + ------- ___ |
11 7 \/ 27 9 | \/ 27 9 7*\/ 3 |
x1 = -- - ---------------------- - ------------------- + I*|- ------------------------- + ----------------------|
3 ______________ 2 | 2 ______________|
/ _____ | / _____ |
/ 44 \/ 177 | / 44 \/ 177 |
18*3 / -- + ------- | 18*3 / -- + ------- |
\/ 27 9 \ \/ 27 9 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} - \frac{7}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{11}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} + \frac{7 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}\right)$$
______________ / ______________ \
/ _____ | / _____ |
/ 44 \/ 177 | ___ / 44 \/ 177 |
3 / -- + ------- |\/ 3 *3 / -- + ------- ___ |
11 7 \/ 27 9 | \/ 27 9 7*\/ 3 |
x2 = -- - ---------------------- - ------------------- + I*|------------------------- - ----------------------|
3 ______________ 2 | 2 ______________|
/ _____ | / _____ |
/ 44 \/ 177 | / 44 \/ 177 |
18*3 / -- + ------- | 18*3 / -- + ------- |
\/ 27 9 \ \/ 27 9 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2} - \frac{7}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{11}{3} + i \left(- \frac{7 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}}{2}\right)$$
______________
/ _____
11 / 44 \/ 177 7
x3 = -- + 3 / -- + ------- + ---------------------
3 \/ 27 9 ______________
/ _____
/ 44 \/ 177
9*3 / -- + -------
\/ 27 9
$$x_{3} = \frac{7}{9 \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}}} + \sqrt[3]{\frac{\sqrt{177}}{9} + \frac{44}{27}} + \frac{11}{3}$$
x3 = 7/(9*(sqrt(177)/9 + 44/27)^(1/3)) + (sqrt(177)/9 + 44/27)^(1/3) + 11/3
Respuesta numérica
[src]
x1 = 5.65896708191699
x2 = 2.6705164590415 - 0.802254557557411*i
x3 = 2.6705164590415 + 0.802254557557411*i
x3 = 2.6705164590415 + 0.802254557557411*i