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Ecuación 3^x+4^x=5^x
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Ecuación (x-2)^4+3*(x-2)^2-10=0
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Ecuación x+2/x=3
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Ecuación x^2=-2
- Expresar {x} en función de y en la ecuación:
- -9*x-15*y=-4
- -13*x+7*y=11
- -7*x-7*y=-14
- 2*x+13*y=19
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Expresiones idénticas
- 3x+ cuatro /x- dos - seis (x- dos)/3x+ cuatro = uno
- 3x más 4 dividir por x menos 2 menos 6(x menos 2) dividir por 3x más 4 es igual a 1
- 3x más cuatro dividir por x menos dos menos seis (x menos dos) dividir por 3x más cuatro es igual a uno
- 3x+4/x-2-6x-2/3x+4=1
- 3x+4 dividir por x-2-6(x-2) dividir por 3x+4=1
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Expresiones semejantes
- 3x+4/x+2-6(x-2)/3x+4=1
- 3x+4/x-2-6(x-2)/3x-4=1
- 3x+4/x-2-6(x+2)/3x+4=1
- 3x+4/x-2+6(x-2)/3x+4=1
- 3x-4/x-2-6(x-2)/3x+4=1
3x+4/x-2-6(x-2)/3x+4=1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 6*(x - 2)
3*x + - - 2 - ---------*x + 4 = 1
x 3
$$\left(- x \frac{6 \left(x - 2\right)}{3} + \left(\left(3 x + \frac{4}{x}\right) - 2\right)\right) + 4 = 1$$
Respuesta rápida
[src]
_________________ / _________________ \
/ _______ | / _______ |
/ 311 \/ 24501 | ___ / 311 \/ 24501 |
3 / --- + --------- | \/ 3 *3 / --- + --------- ___ |
7 55 \/ 108 72 | \/ 108 72 55*\/ 3 |
x1 = - - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------|
6 _________________ 2 | 2 _________________|
/ _______ | / _______ |
/ 311 \/ 24501 | / 311 \/ 24501 |
72*3 / --- + --------- | 72*3 / --- + --------- |
\/ 108 72 \ \/ 108 72 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} - \frac{55}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} + \frac{55 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}\right)$$
_________________ / _________________ \
/ _______ | / _______ |
/ 311 \/ 24501 | ___ / 311 \/ 24501 |
3 / --- + --------- |\/ 3 *3 / --- + --------- ___ |
7 55 \/ 108 72 | \/ 108 72 55*\/ 3 |
x2 = - - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------|
6 _________________ 2 | 2 _________________|
/ _______ | / _______ |
/ 311 \/ 24501 | / 311 \/ 24501 |
72*3 / --- + --------- | 72*3 / --- + --------- |
\/ 108 72 \ \/ 108 72 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} - \frac{55}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + i \left(- \frac{55 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2}\right)$$
_________________
/ _______
7 / 311 \/ 24501 55
x3 = - + 3 / --- + --------- + -------------------------
6 \/ 108 72 _________________
/ _______
/ 311 \/ 24501
36*3 / --- + ---------
\/ 108 72
$$x_{3} = \frac{55}{36 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}$$
x3 = 55/(36*(sqrt(24501)/72 + 311/108)^(1/3)) + 7/6 + (sqrt(24501)/72 + 311/108)^(1/3)
Suma y producto de raíces
[src]
suma
_________________ / _________________ \ _________________ / _________________ \
/ _______ | / _______ | / _______ | / _______ |
/ 311 \/ 24501 | ___ / 311 \/ 24501 | / 311 \/ 24501 | ___ / 311 \/ 24501 | _________________
3 / --- + --------- | \/ 3 *3 / --- + --------- ___ | 3 / --- + --------- |\/ 3 *3 / --- + --------- ___ | / _______
7 55 \/ 108 72 | \/ 108 72 55*\/ 3 | 7 55 \/ 108 72 | \/ 108 72 55*\/ 3 | 7 / 311 \/ 24501 55
- - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------| + - - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------| + - + 3 / --- + --------- + -------------------------
6 _________________ 2 | 2 _________________| 6 _________________ 2 | 2 _________________| 6 \/ 108 72 _________________
/ _______ | / _______ | / _______ | / _______ | / _______
/ 311 \/ 24501 | / 311 \/ 24501 | / 311 \/ 24501 | / 311 \/ 24501 | / 311 \/ 24501
72*3 / --- + --------- | 72*3 / --- + --------- | 72*3 / --- + --------- | 72*3 / --- + --------- | 36*3 / --- + ---------
\/ 108 72 \ \/ 108 72 / \/ 108 72 \ \/ 108 72 / \/ 108 72
$$\left(\frac{55}{36 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} - \frac{55}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} + \frac{55 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} - \frac{55}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + i \left(- \frac{55 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2}\right)\right)\right)$$
=
/ _________________ \ / _________________ \
| / _______ | | / _______ |
| ___ / 311 \/ 24501 | | ___ / 311 \/ 24501 |
|\/ 3 *3 / --- + --------- ___ | | \/ 3 *3 / --- + --------- ___ |
7 | \/ 108 72 55*\/ 3 | | \/ 108 72 55*\/ 3 |
- + I*|---------------------------- - -------------------------| + I*|- ---------------------------- + -------------------------|
2 | 2 _________________| | 2 _________________|
| / _______ | | / _______ |
| / 311 \/ 24501 | | / 311 \/ 24501 |
| 72*3 / --- + --------- | | 72*3 / --- + --------- |
\ \/ 108 72 / \ \/ 108 72 /
$$\frac{7}{2} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} + \frac{55 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}\right) + i \left(- \frac{55 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2}\right)$$
producto
/ _________________ / _________________ \\ / _________________ / _________________ \\ | / _______ | / _______ || | / _______ | / _______ || | / 311 \/ 24501 | ___ / 311 \/ 24501 || | / 311 \/ 24501 | ___ / 311 \/ 24501 || / _________________ \ | 3 / --- + --------- | \/ 3 *3 / --- + --------- ___ || | 3 / --- + --------- |\/ 3 *3 / --- + --------- ___ || | / _______ | |7 55 \/ 108 72 | \/ 108 72 55*\/ 3 || |7 55 \/ 108 72 | \/ 108 72 55*\/ 3 || |7 / 311 \/ 24501 55 | |- - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------||*|- - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------||*|- + 3 / --- + --------- + -------------------------| |6 _________________ 2 | 2 _________________|| |6 _________________ 2 | 2 _________________|| |6 \/ 108 72 _________________| | / _______ | / _______ || | / _______ | / _______ || | / _______ | | / 311 \/ 24501 | / 311 \/ 24501 || | / 311 \/ 24501 | / 311 \/ 24501 || | / 311 \/ 24501 | | 72*3 / --- + --------- | 72*3 / --- + --------- || | 72*3 / --- + --------- | 72*3 / --- + --------- || | 36*3 / --- + --------- | \ \/ 108 72 \ \/ 108 72 // \ \/ 108 72 \ \/ 108 72 // \ \/ 108 72 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} - \frac{55}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + i \left(- \frac{55 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} - \frac{55}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}{2} + \frac{55 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}}\right)\right) \left(\frac{55}{36 \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}} + \frac{7}{6} + \sqrt[3]{\frac{\sqrt{24501}}{72} + \frac{311}{108}}\right)$$
=
2
$$2$$
2
Respuesta numérica
[src]
x1 = -0.136506349296774 - 0.715154805110343*i
x2 = -0.136506349296774 + 0.715154805110343*i
x3 = 3.77301269859355
x3 = 3.77301269859355