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Expresiones semejantes
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- x-3/x-1=x^2-5/2x+2
- (x-3)/(x-1)=0
x-3/x-1=x^2-5/2x-2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 5*x
x - - - 1 = x - --- - 2
x 2
$$\left(x - \frac{3}{x}\right) - 1 = \left(x^{2} - \frac{5 x}{2}\right) - 2$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
61*re|---------------------------------------| |61*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| __________________| | | __________________| | |6*\/ 5721 || | |6*\/ 5721 ||| | |6*\/ 5721 || | |6*\/ 5721 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
|| 1 I*\/ 3 | / 145 I*\/ 5721 | | || 1 I*\/ 3 | / 145 I*\/ 5721 | ____ | \ 145 /| _____ | \ 145 /|| ____ | \ 145 /| _____ | \ 145 /|
||- - - -------|*3 / --- + ---------- | | ||- - - -------|*3 / --- + ---------- | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------|
7 \\ 2 2 / \/ 216 36 / | \\ 2 2 / \/ 216 36 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = - + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - -----------------------------| - ---------------------------- + -----------------------------
6 36 \ 36 12 12 / 12 12
$$x_{1} = - \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{7}{6} + i \left(- \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36}\right)$$
/ 1 \ / / 1 \ \
61*re|---------------------------------------| |61*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| __________________| | | __________________| | |6*\/ 5721 || | |6*\/ 5721 ||| | |6*\/ 5721 || | |6*\/ 5721 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
|| 1 I*\/ 3 | / 145 I*\/ 5721 | | || 1 I*\/ 3 | / 145 I*\/ 5721 | ____ | \ 145 /| _____ | \ 145 /|| ____ | \ 145 /| _____ | \ 145 /|
||- - + -------|*3 / --- + ---------- | | ||- - + -------|*3 / --- + ---------- | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------|
7 \\ 2 2 / \/ 216 36 / | \\ 2 2 / \/ 216 36 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = - + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + -----------------------------| - ---------------------------- - -----------------------------
6 36 \ 36 12 12 / 12 12
$$x_{2} = \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} - \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} - \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{7}{6} + i \left(\frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12}\right)$$
__________________
/ ______
7 / 145 I*\/ 5721 61
x3 = - + 3 / --- + ---------- + --------------------------
6 \/ 216 36 __________________
/ ______
/ 145 I*\/ 5721
36*3 / --- + ----------
\/ 216 36
$$x_{3} = \frac{7}{6} + \frac{61}{36 \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}} + \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}$$
x3 = 7/6 + 61/(36*(145/216 + sqrt(5721)*i/36)^(1/3)) + (145/216 + sqrt(5721)*i/36)^(1/3)
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
61*re|---------------------------------------| |61*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ 61*re|---------------------------------------| |61*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| __________________| | | __________________| | |6*\/ 5721 || | |6*\/ 5721 ||| | |6*\/ 5721 || | |6*\/ 5721 || | __________________| | | __________________| | |6*\/ 5721 || | |6*\/ 5721 ||| | |6*\/ 5721 || | |6*\/ 5721 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
|| 1 I*\/ 3 | / 145 I*\/ 5721 | | || 1 I*\/ 3 | / 145 I*\/ 5721 | ____ | \ 145 /| _____ | \ 145 /|| ____ | \ 145 /| _____ | \ 145 /| || 1 I*\/ 3 | / 145 I*\/ 5721 | | || 1 I*\/ 3 | / 145 I*\/ 5721 | ____ | \ 145 /| _____ | \ 145 /|| ____ | \ 145 /| _____ | \ 145 /| __________________
||- - - -------|*3 / --- + ---------- | | ||- - - -------|*3 / --- + ---------- | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------| ||- - + -------|*3 / --- + ---------- | | ||- - + -------|*3 / --- + ---------- | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------| / ______
7 \\ 2 2 / \/ 216 36 / | \\ 2 2 / \/ 216 36 / \ 3 / \ 3 /| \ 3 / \ 3 / 7 \\ 2 2 / \/ 216 36 / | \\ 2 2 / \/ 216 36 / \ 3 / \ 3 /| \ 3 / \ 3 / 7 / 145 I*\/ 5721 61
- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - -----------------------------| - ---------------------------- + ----------------------------- + - + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + -----------------------------| - ---------------------------- - ----------------------------- + - + 3 / --- + ---------- + --------------------------
6 36 \ 36 12 12 / 12 12 6 36 \ 36 12 12 / 12 12 6 \/ 216 36 __________________
/ ______
/ 145 I*\/ 5721
36*3 / --- + ----------
\/ 216 36
$$\left(\frac{7}{6} + \frac{61}{36 \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}} + \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}\right) + \left(\left(\frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} - \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} - \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{7}{6} + i \left(\frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12}\right)\right) + \left(- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{7}{6} + i \left(- \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
61*re|---------------------------------------| 61*re|---------------------------------------| |61*im|---------------------------------------| / / ______\\ / / ______\\| |61*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\
| __________________| | __________________| | | __________________| | |6*\/ 5721 || | |6*\/ 5721 ||| | | __________________| | |6*\/ 5721 || | |6*\/ 5721 ||| | |6*\/ 5721 ||
|/ ___\ / ______ | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------||
__________________ || 1 I*\/ 3 | / 145 I*\/ 5721 | || 1 I*\/ 3 | / 145 I*\/ 5721 | | || 1 I*\/ 3 | / 145 I*\/ 5721 | ____ | \ 145 /| _____ | \ 145 /|| | || 1 I*\/ 3 | / 145 I*\/ 5721 | ____ | \ 145 /| _____ | \ 145 /|| ____ | \ 145 /|
/ ______ ||- - + -------|*3 / --- + ---------- | ||- - - -------|*3 / --- + ---------- | | ||- - + -------|*3 / --- + ---------- | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| | ||- - - -------|*3 / --- + ---------- | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------|
7 / 145 I*\/ 5721 61 \\ 2 2 / \/ 216 36 / \\ 2 2 / \/ 216 36 / | \\ 2 2 / \/ 216 36 / \ 3 / \ 3 /| | \\ 2 2 / \/ 216 36 / \ 3 / \ 3 /| \ 3 /
- + 3 / --- + ---------- + -------------------------- + ---------------------------------------------- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + -----------------------------| + I*|---------------------------------------------- - ---------------------------- - -----------------------------| - ----------------------------
2 \/ 216 36 __________________ 36 36 \ 36 12 12 / \ 36 12 12 / 6
/ ______
/ 145 I*\/ 5721
36*3 / --- + ----------
\/ 216 36
$$- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{6} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} + \frac{7}{2} + \frac{61}{36 \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}} + i \left(- \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36}\right) + i \left(\frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12}\right) + \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 61*re|---------------------------------------| |61*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\| | 61*re|---------------------------------------| |61*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\|
| | __________________| | | __________________| | |6*\/ 5721 || | |6*\/ 5721 ||| | |6*\/ 5721 || | |6*\/ 5721 ||| | | __________________| | | __________________| | |6*\/ 5721 || | |6*\/ 5721 ||| | |6*\/ 5721 || | |6*\/ 5721 |||
| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|||
| || 1 I*\/ 3 | / 145 I*\/ 5721 | | || 1 I*\/ 3 | / 145 I*\/ 5721 | ____ | \ 145 /| _____ | \ 145 /|| ____ | \ 145 /| _____ | \ 145 /|| | || 1 I*\/ 3 | / 145 I*\/ 5721 | | || 1 I*\/ 3 | / 145 I*\/ 5721 | ____ | \ 145 /| _____ | \ 145 /|| ____ | \ 145 /| _____ | \ 145 /|| / __________________ \
| ||- - - -------|*3 / --- + ---------- | | ||- - - -------|*3 / --- + ---------- | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------|| | ||- - + -------|*3 / --- + ---------- | | ||- - + -------|*3 / --- + ---------- | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------|| | / ______ |
|7 \\ 2 2 / \/ 216 36 / | \\ 2 2 / \/ 216 36 / \ 3 / \ 3 /| \ 3 / \ 3 /| |7 \\ 2 2 / \/ 216 36 / | \\ 2 2 / \/ 216 36 / \ 3 / \ 3 /| \ 3 / \ 3 /| |7 / 145 I*\/ 5721 61 |
|- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - -----------------------------| - ---------------------------- + -----------------------------|*|- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + -----------------------------| - ---------------------------- - -----------------------------|*|- + 3 / --- + ---------- + --------------------------|
\6 36 \ 36 12 12 / 12 12 / \6 36 \ 36 12 12 / 12 12 / |6 \/ 216 36 __________________|
| / ______ |
| / 145 I*\/ 5721 |
| 36*3 / --- + ---------- |
\ \/ 216 36 /
$$\left(- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{7}{6} + i \left(- \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36}\right)\right) \left(\frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} - \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} - \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{7}{6} + i \left(\frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}}\right)}}{36} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}}{12}\right)\right) \left(\frac{7}{6} + \frac{61}{36 \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}} + \sqrt[3]{\frac{145}{216} + \frac{\sqrt{5721} i}{36}}\right)$$
=
/ / / ______\\ / / ______\\\
| | |6*\/ 5721 || | |6*\/ 5721 |||
/ ____________________ / ____________________\\ | |2*atan|----------|| |atan|----------|||
| 3 / ______ | 3 / ______ || | | \ 145 /| ____ | \ 145 /||
\61 + \/ 145 + 6*I*\/ 5721 *\7 + \/ 145 + 6*I*\/ 5721 //*|-12 + 122*cos|------------------| - 14*\/ 61 *cos|----------------||
\ \ 3 / \ 3 //
----------------------------------------------------------------------------------------------------------------------------------
____________________
3 / ______
216*\/ 145 + 6*I*\/ 5721
$$\frac{\left(61 + \left(7 + \sqrt[3]{145 + 6 \sqrt{5721} i}\right) \sqrt[3]{145 + 6 \sqrt{5721} i}\right) \left(- 14 \sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)} - 12 + 122 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{6 \sqrt{5721}}{145} \right)}}{3} \right)}\right)}{216 \sqrt[3]{145 + 6 \sqrt{5721} i}}$$
(61 + (145 + 6*i*sqrt(5721))^(1/3)*(7 + (145 + 6*i*sqrt(5721))^(1/3)))*(-12 + 122*cos(2*atan(6*sqrt(5721)/145)/3) - 14*sqrt(61)*cos(atan(6*sqrt(5721)/145)/3))/(216*(145 + 6*i*sqrt(5721))^(1/3))
Respuesta numérica
[src]
x1 = 0.898767717312578 + 0.e-20*i
x2 = -0.942039861710383 + 0.e-20*i
x3 = 3.5432721443978 - 0.e-21*i
x3 = 3.5432721443978 - 0.e-21*i