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- La ecuación:
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Ecuación 2x-4=8+2x
-
Ecuación x/4+x=-5
-
Ecuación 18-x^2=14
-
Ecuación e^x=1
- Expresar {x} en función de y en la ecuación:
- -1*x+4*y=-10
- -14*x-8*y=20
- 11*x-2*y=-9
- -6*x+1*y=-5
-
Expresiones idénticas
- uno /(x- cuatro)^ dos - siete /x- cuatro + diez = cero
- 1 dividir por (x menos 4) al cuadrado menos 7 dividir por x menos 4 más 10 es igual a 0
- uno dividir por (x menos cuatro) en el grado dos menos siete dividir por x menos cuatro más diez es igual a cero
- 1/(x-4)2-7/x-4+10=0
- 1/x-42-7/x-4+10=0
- 1/(x-4)²-7/x-4+10=0
- 1/(x-4) en el grado 2-7/x-4+10=0
- 1/x-4^2-7/x-4+10=0
- 1/(x-4)^2-7/x-4+10=O
- 1 dividir por (x-4)^2-7 dividir por x-4+10=0
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Expresiones semejantes
- 1/(x-4)^2+7/x-4+10=0
- 1/(x-4)^2-7/x-4-10=0
- 1/(x-4)^2-7/x+4+10=0
- 1/(x+4)^2-7/x-4+10=0
1/(x-4)^2-7/x-4+10=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
1 7
-------- - - - 4 + 10 = 0
2 x
(x - 4)
$$\left(\left(\frac{1}{\left(x - 4\right)^{2}} - \frac{7}{x}\right) - 4\right) + 10 = 0$$
Suma y producto de raíces
[src]
suma
___________________ / ___________________\ ___________________ / ___________________ \ ___________________
/ ________ | / ________ | / ________ | / ________ | / ________
/ 3199 \/ 259653 | ___ / 3199 \/ 259653 | / 3199 \/ 259653 | ___ / 3199 \/ 259653 | / 3199 \/ 259653
3 / ---- + ---------- | ___ \/ 3 *3 / ---- + ---------- | 3 / ---- + ---------- | \/ 3 *3 / ---- + ---------- ___ | 3 / ---- + ----------
55 \/ 108 24 271 | 271*\/ 3 \/ 108 24 | 55 \/ 108 24 271 | \/ 108 24 271*\/ 3 | 55 271 \/ 108 24
-- + ------------------------ + ---------------------------- + I*|- ---------------------------- + ------------------------------| + -- + ------------------------ + ---------------------------- + I*|- ------------------------------ + ----------------------------| + -- - ---------------------------- - ------------------------
18 6 ___________________ | ___________________ 6 | 18 6 ___________________ | 6 ___________________| 18 ___________________ 3
/ ________ | / ________ | / ________ | / ________ | / ________
/ 3199 \/ 259653 | / 3199 \/ 259653 | / 3199 \/ 259653 | / 3199 \/ 259653 | / 3199 \/ 259653
216*3 / ---- + ---------- | 216*3 / ---- + ---------- | 216*3 / ---- + ---------- | 216*3 / ---- + ---------- | 108*3 / ---- + ----------
\/ 108 24 \ \/ 108 24 / \/ 108 24 \ \/ 108 24 / \/ 108 24
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{3} - \frac{271}{108 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{55}{18}\right) + \left(\left(\frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}\right)\right) + \left(\frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6}\right)\right)\right)$$
=
/ ___________________\ / ___________________ \
| / ________ | | / ________ |
| ___ / 3199 \/ 259653 | | ___ / 3199 \/ 259653 |
| ___ \/ 3 *3 / ---- + ---------- | | \/ 3 *3 / ---- + ---------- ___ |
55 | 271*\/ 3 \/ 108 24 | | \/ 108 24 271*\/ 3 |
-- + I*|- ---------------------------- + ------------------------------| + I*|- ------------------------------ + ----------------------------|
6 | ___________________ 6 | | 6 ___________________|
| / ________ | | / ________ |
| / 3199 \/ 259653 | | / 3199 \/ 259653 |
| 216*3 / ---- + ---------- | | 216*3 / ---- + ---------- |
\ \/ 108 24 / \ \/ 108 24 /
$$\frac{55}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}\right) + i \left(- \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6}\right)$$
producto
/ ___________________ / ___________________\\ / ___________________ / ___________________ \\ / ___________________\ | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / 3199 \/ 259653 | ___ / 3199 \/ 259653 || | / 3199 \/ 259653 | ___ / 3199 \/ 259653 || | / 3199 \/ 259653 | | 3 / ---- + ---------- | ___ \/ 3 *3 / ---- + ---------- || | 3 / ---- + ---------- | \/ 3 *3 / ---- + ---------- ___ || | 3 / ---- + ---------- | |55 \/ 108 24 271 | 271*\/ 3 \/ 108 24 || |55 \/ 108 24 271 | \/ 108 24 271*\/ 3 || |55 271 \/ 108 24 | |-- + ------------------------ + ---------------------------- + I*|- ---------------------------- + ------------------------------||*|-- + ------------------------ + ---------------------------- + I*|- ------------------------------ + ----------------------------||*|-- - ---------------------------- - ------------------------| |18 6 ___________________ | ___________________ 6 || |18 6 ___________________ | 6 ___________________|| |18 ___________________ 3 | | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / 3199 \/ 259653 | / 3199 \/ 259653 || | / 3199 \/ 259653 | / 3199 \/ 259653 || | / 3199 \/ 259653 | | 216*3 / ---- + ---------- | 216*3 / ---- + ---------- || | 216*3 / ---- + ---------- | 216*3 / ---- + ---------- || | 108*3 / ---- + ---------- | \ \/ 108 24 \ \/ 108 24 // \ \/ 108 24 \ \/ 108 24 // \ \/ 108 24 /
$$\left(\frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6}\right)\right) \left(\frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{3} - \frac{271}{108 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{55}{18}\right)$$
=
56/3
$$\frac{56}{3}$$
56/3
Respuesta rápida
[src]
___________________ / ___________________\
/ ________ | / ________ |
/ 3199 \/ 259653 | ___ / 3199 \/ 259653 |
3 / ---- + ---------- | ___ \/ 3 *3 / ---- + ---------- |
55 \/ 108 24 271 | 271*\/ 3 \/ 108 24 |
x1 = -- + ------------------------ + ---------------------------- + I*|- ---------------------------- + ------------------------------|
18 6 ___________________ | ___________________ 6 |
/ ________ | / ________ |
/ 3199 \/ 259653 | / 3199 \/ 259653 |
216*3 / ---- + ---------- | 216*3 / ---- + ---------- |
\/ 108 24 \ \/ 108 24 /
$$x_{1} = \frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6}\right)$$
___________________ / ___________________ \
/ ________ | / ________ |
/ 3199 \/ 259653 | ___ / 3199 \/ 259653 |
3 / ---- + ---------- | \/ 3 *3 / ---- + ---------- ___ |
55 \/ 108 24 271 | \/ 108 24 271*\/ 3 |
x2 = -- + ------------------------ + ---------------------------- + I*|- ------------------------------ + ----------------------------|
18 6 ___________________ | 6 ___________________|
/ ________ | / ________ |
/ 3199 \/ 259653 | / 3199 \/ 259653 |
216*3 / ---- + ---------- | 216*3 / ---- + ---------- |
\/ 108 24 \ \/ 108 24 /
$$x_{2} = \frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}\right)$$
___________________
/ ________
/ 3199 \/ 259653
3 / ---- + ----------
55 271 \/ 108 24
x3 = -- - ---------------------------- - ------------------------
18 ___________________ 3
/ ________
/ 3199 \/ 259653
108*3 / ---- + ----------
\/ 108 24
$$x_{3} = - \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{3} - \frac{271}{108 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{55}{18}$$
x3 = -(sqrt(259653)/24 + 3199/108)^(1/3)/3 - 271/(108*(sqrt(259653)/24 + 3199/108)^(1/3)) + 55/18
Respuesta numérica
[src]
x1 = 4.01167510882973 + 0.482943621140577*i
x2 = 4.01167510882973 - 0.482943621140577*i
x3 = 1.1433164490072
x3 = 1.1433164490072
Gráfico