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Ecuación (6*x+8)/2+5=5*x/3
- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
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- 1/(x-3)2-8/x-3+15=0
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- 1/(x-3) en el grado 2-8/x-3+15=0
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Expresiones semejantes
- 1/(x-3)^2-8/x-3-15=0
- 1/(x-3)^2-8/x+3+15=0
- 1/(x+3)^2-8/x-3+15=0
- 1/(x-3)^2+8/x-3+15=0
1/(x-3)^2-8/x-3+15=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
1 8
-------- - - - 3 + 15 = 0
2 x
(x - 3)
$$\left(\left(\frac{1}{\left(x - 3\right)^{2}} - \frac{8}{x}\right) - 3\right) + 15 = 0$$
Respuesta rápida
[src]
_________________ / _________________\
/ _______ | / _______ |
/ 821 \/ 52413 | ___ / 821 \/ 52413 |
3 / --- + --------- | ___ \/ 3 *3 / --- + --------- |
20 \/ 54 24 187 | 187*\/ 3 \/ 54 24 |
x1 = -- + ---------------------- + -------------------------- + I*|- -------------------------- + ----------------------------|
9 6 _________________ | _________________ 6 |
/ _______ | / _______ |
/ 821 \/ 52413 | / 821 \/ 52413 |
216*3 / --- + --------- | 216*3 / --- + --------- |
\/ 54 24 \ \/ 54 24 /
$$x_{1} = \frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6}\right)$$
_________________ / _________________ \
/ _______ | / _______ |
/ 821 \/ 52413 | ___ / 821 \/ 52413 |
3 / --- + --------- | \/ 3 *3 / --- + --------- ___ |
20 \/ 54 24 187 | \/ 54 24 187*\/ 3 |
x2 = -- + ---------------------- + -------------------------- + I*|- ---------------------------- + --------------------------|
9 6 _________________ | 6 _________________|
/ _______ | / _______ |
/ 821 \/ 52413 | / 821 \/ 52413 |
216*3 / --- + --------- | 216*3 / --- + --------- |
\/ 54 24 \ \/ 54 24 /
$$x_{2} = \frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}\right)$$
_________________
/ _______
/ 821 \/ 52413
3 / --- + ---------
20 187 \/ 54 24
x3 = -- - -------------------------- - ----------------------
9 _________________ 3
/ _______
/ 821 \/ 52413
108*3 / --- + ---------
\/ 54 24
$$x_{3} = - \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{3} - \frac{187}{108 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{20}{9}$$
x3 = -(sqrt(52413)/24 + 821/54)^(1/3)/3 - 187/(108*(sqrt(52413)/24 + 821/54)^(1/3)) + 20/9
Suma y producto de raíces
[src]
suma
_________________ / _________________\ _________________ / _________________ \ _________________
/ _______ | / _______ | / _______ | / _______ | / _______
/ 821 \/ 52413 | ___ / 821 \/ 52413 | / 821 \/ 52413 | ___ / 821 \/ 52413 | / 821 \/ 52413
3 / --- + --------- | ___ \/ 3 *3 / --- + --------- | 3 / --- + --------- | \/ 3 *3 / --- + --------- ___ | 3 / --- + ---------
20 \/ 54 24 187 | 187*\/ 3 \/ 54 24 | 20 \/ 54 24 187 | \/ 54 24 187*\/ 3 | 20 187 \/ 54 24
-- + ---------------------- + -------------------------- + I*|- -------------------------- + ----------------------------| + -- + ---------------------- + -------------------------- + I*|- ---------------------------- + --------------------------| + -- - -------------------------- - ----------------------
9 6 _________________ | _________________ 6 | 9 6 _________________ | 6 _________________| 9 _________________ 3
/ _______ | / _______ | / _______ | / _______ | / _______
/ 821 \/ 52413 | / 821 \/ 52413 | / 821 \/ 52413 | / 821 \/ 52413 | / 821 \/ 52413
216*3 / --- + --------- | 216*3 / --- + --------- | 216*3 / --- + --------- | 216*3 / --- + --------- | 108*3 / --- + ---------
\/ 54 24 \ \/ 54 24 / \/ 54 24 \ \/ 54 24 / \/ 54 24
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{3} - \frac{187}{108 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{20}{9}\right) + \left(\left(\frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}\right)\right) + \left(\frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6}\right)\right)\right)$$
=
/ _________________\ / _________________ \
| / _______ | | / _______ |
| ___ / 821 \/ 52413 | | ___ / 821 \/ 52413 |
| ___ \/ 3 *3 / --- + --------- | | \/ 3 *3 / --- + --------- ___ |
20 | 187*\/ 3 \/ 54 24 | | \/ 54 24 187*\/ 3 |
-- + I*|- -------------------------- + ----------------------------| + I*|- ---------------------------- + --------------------------|
3 | _________________ 6 | | 6 _________________|
| / _______ | | / _______ |
| / 821 \/ 52413 | | / 821 \/ 52413 |
| 216*3 / --- + --------- | | 216*3 / --- + --------- |
\ \/ 54 24 / \ \/ 54 24 /
$$\frac{20}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}\right) + i \left(- \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6}\right)$$
producto
/ _________________ / _________________\\ / _________________ / _________________ \\ / _________________\ | / _______ | / _______ || | / _______ | / _______ || | / _______ | | / 821 \/ 52413 | ___ / 821 \/ 52413 || | / 821 \/ 52413 | ___ / 821 \/ 52413 || | / 821 \/ 52413 | | 3 / --- + --------- | ___ \/ 3 *3 / --- + --------- || | 3 / --- + --------- | \/ 3 *3 / --- + --------- ___ || | 3 / --- + --------- | |20 \/ 54 24 187 | 187*\/ 3 \/ 54 24 || |20 \/ 54 24 187 | \/ 54 24 187*\/ 3 || |20 187 \/ 54 24 | |-- + ---------------------- + -------------------------- + I*|- -------------------------- + ----------------------------||*|-- + ---------------------- + -------------------------- + I*|- ---------------------------- + --------------------------||*|-- - -------------------------- - ----------------------| |9 6 _________________ | _________________ 6 || |9 6 _________________ | 6 _________________|| |9 _________________ 3 | | / _______ | / _______ || | / _______ | / _______ || | / _______ | | / 821 \/ 52413 | / 821 \/ 52413 || | / 821 \/ 52413 | / 821 \/ 52413 || | / 821 \/ 52413 | | 216*3 / --- + --------- | 216*3 / --- + --------- || | 216*3 / --- + --------- | 216*3 / --- + --------- || | 108*3 / --- + --------- | \ \/ 54 24 \ \/ 54 24 // \ \/ 54 24 \ \/ 54 24 // \ \/ 54 24 /
$$\left(\frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6}\right)\right) \left(\frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{3} - \frac{187}{108 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{20}{9}\right)$$
=
6
$$6$$
6
Respuesta numérica
[src]
x1 = 3.00498310973485 + 0.326592007828122*i
x2 = 3.00498310973485 - 0.326592007828122*i
x3 = 0.65670044719696
x3 = 0.65670044719696
Gráfico