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Expresiones idénticas
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Expresiones semejantes
- x+2/x+1-x-3/x-1=5/x^2-1
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- x+2/x+1+x-3/x+1=5/x^2-1
- x-2/x+1+x-3/x-1=5/x^2-1
- x+2/x-1+x-3/x-1=5/x^2-1
x+2/x+1+x-3/x-1=5/x^2-1 la ecuación
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Solución
Ha introducido
[src]
2 3 5
x + - + 1 + x - - - 1 = -- - 1
x x 2
x
$$\left(\left(x + \left(\left(x + \frac{2}{x}\right) + 1\right)\right) - \frac{3}{x}\right) - 1 = -1 + \frac{5}{x^{2}}$$
Suma y producto de raíces
[src]
suma
_______________ / _______________ \ _______________ / _______________ \
/ ______ | / ______ | / ______ | / ______ |
/ 65 \/ 7473 | ___ / 65 \/ 7473 | / 65 \/ 7473 | ___ / 65 \/ 7473 | _______________
3 / -- + -------- | \/ 3 *3 / -- + -------- ___ | 3 / -- + -------- |\/ 3 *3 / -- + -------- ___ | / ______
1 7 \/ 54 72 | \/ 54 72 7*\/ 3 | 1 7 \/ 54 72 | \/ 54 72 7*\/ 3 | 1 / 65 \/ 7473 7
- - - ----------------------- - -------------------- + I*|- -------------------------- + -----------------------| + - - - ----------------------- - -------------------- + I*|-------------------------- - -----------------------| + - - + 3 / -- + -------- + -----------------------
6 _______________ 2 | 2 _______________| 6 _______________ 2 | 2 _______________| 6 \/ 54 72 _______________
/ ______ | / ______ | / ______ | / ______ | / ______
/ 65 \/ 7473 | / 65 \/ 7473 | / 65 \/ 7473 | / 65 \/ 7473 | / 65 \/ 7473
72*3 / -- + -------- | 72*3 / -- + -------- | 72*3 / -- + -------- | 72*3 / -- + -------- | 36*3 / -- + --------
\/ 54 72 \ \/ 54 72 / \/ 54 72 \ \/ 54 72 / \/ 54 72
$$\left(- \frac{1}{6} + \frac{7}{36 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} - \frac{1}{6} - \frac{7}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} + \frac{7 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} - \frac{1}{6} - \frac{7}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + i \left(- \frac{7 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2}\right)\right)\right)$$
=
/ _______________ \ / _______________ \
| / ______ | | / ______ |
| ___ / 65 \/ 7473 | | ___ / 65 \/ 7473 |
|\/ 3 *3 / -- + -------- ___ | | \/ 3 *3 / -- + -------- ___ |
1 | \/ 54 72 7*\/ 3 | | \/ 54 72 7*\/ 3 |
- - + I*|-------------------------- - -----------------------| + I*|- -------------------------- + -----------------------|
2 | 2 _______________| | 2 _______________|
| / ______ | | / ______ |
| / 65 \/ 7473 | | / 65 \/ 7473 |
| 72*3 / -- + -------- | | 72*3 / -- + -------- |
\ \/ 54 72 / \ \/ 54 72 /
$$- \frac{1}{2} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} + \frac{7 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}\right) + i \left(- \frac{7 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2}\right)$$
producto
/ _______________ / _______________ \\ / _______________ / _______________ \\ | / ______ | / ______ || | / ______ | / ______ || | / 65 \/ 7473 | ___ / 65 \/ 7473 || | / 65 \/ 7473 | ___ / 65 \/ 7473 || / _______________ \ | 3 / -- + -------- | \/ 3 *3 / -- + -------- ___ || | 3 / -- + -------- |\/ 3 *3 / -- + -------- ___ || | / ______ | | 1 7 \/ 54 72 | \/ 54 72 7*\/ 3 || | 1 7 \/ 54 72 | \/ 54 72 7*\/ 3 || | 1 / 65 \/ 7473 7 | |- - - ----------------------- - -------------------- + I*|- -------------------------- + -----------------------||*|- - - ----------------------- - -------------------- + I*|-------------------------- - -----------------------||*|- - + 3 / -- + -------- + -----------------------| | 6 _______________ 2 | 2 _______________|| | 6 _______________ 2 | 2 _______________|| | 6 \/ 54 72 _______________| | / ______ | / ______ || | / ______ | / ______ || | / ______ | | / 65 \/ 7473 | / 65 \/ 7473 || | / 65 \/ 7473 | / 65 \/ 7473 || | / 65 \/ 7473 | | 72*3 / -- + -------- | 72*3 / -- + -------- || | 72*3 / -- + -------- | 72*3 / -- + -------- || | 36*3 / -- + -------- | \ \/ 54 72 \ \/ 54 72 // \ \/ 54 72 \ \/ 54 72 // \ \/ 54 72 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} - \frac{1}{6} - \frac{7}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + i \left(- \frac{7 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} - \frac{1}{6} - \frac{7}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} + \frac{7 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}\right)\right) \left(- \frac{1}{6} + \frac{7}{36 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}\right)$$
=
5/2
$$\frac{5}{2}$$
5/2
Respuesta rápida
[src]
_______________ / _______________ \
/ ______ | / ______ |
/ 65 \/ 7473 | ___ / 65 \/ 7473 |
3 / -- + -------- | \/ 3 *3 / -- + -------- ___ |
1 7 \/ 54 72 | \/ 54 72 7*\/ 3 |
x1 = - - - ----------------------- - -------------------- + I*|- -------------------------- + -----------------------|
6 _______________ 2 | 2 _______________|
/ ______ | / ______ |
/ 65 \/ 7473 | / 65 \/ 7473 |
72*3 / -- + -------- | 72*3 / -- + -------- |
\/ 54 72 \ \/ 54 72 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} - \frac{1}{6} - \frac{7}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} + \frac{7 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}\right)$$
_______________ / _______________ \
/ ______ | / ______ |
/ 65 \/ 7473 | ___ / 65 \/ 7473 |
3 / -- + -------- |\/ 3 *3 / -- + -------- ___ |
1 7 \/ 54 72 | \/ 54 72 7*\/ 3 |
x2 = - - - ----------------------- - -------------------- + I*|-------------------------- - -----------------------|
6 _______________ 2 | 2 _______________|
/ ______ | / ______ |
/ 65 \/ 7473 | / 65 \/ 7473 |
72*3 / -- + -------- | 72*3 / -- + -------- |
\/ 54 72 \ \/ 54 72 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2} - \frac{1}{6} - \frac{7}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + i \left(- \frac{7 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}}{2}\right)$$
_______________
/ ______
1 / 65 \/ 7473 7
x3 = - - + 3 / -- + -------- + -----------------------
6 \/ 54 72 _______________
/ ______
/ 65 \/ 7473
36*3 / -- + --------
\/ 54 72
$$x_{3} = - \frac{1}{6} + \frac{7}{36 \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}} + \sqrt[3]{\frac{\sqrt{7473}}{72} + \frac{65}{54}}$$
x3 = -1/6 + 7/(36*(sqrt(7473)/72 + 65/54)^(1/3)) + (sqrt(7473)/72 + 65/54)^(1/3)
Respuesta numérica
[src]
x1 = -0.909075336774673 - 1.03449435330565*i
x2 = -0.909075336774673 + 1.03449435330565*i
x3 = 1.31815067354935
x3 = 1.31815067354935