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Ecuación x+9=0
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Ecuación 2x^2+7x-9=0
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Ecuación 5*x^2+9*x=0
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Ecuación 3x^2=2x+x^3
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -14*x+4*y=-16
- 11*x-9*y=-4
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Expresiones idénticas
- (x- uno)^ dos *(x- cinco)- seis - nueve *(x- cinco)- dos *(x+ uno)= cero
- (x menos 1) al cuadrado multiplicar por (x menos 5) menos 6 menos 9 multiplicar por (x menos 5) menos 2 multiplicar por (x más 1) es igual a 0
- (x menos uno) en el grado dos multiplicar por (x menos cinco) menos seis menos nueve multiplicar por (x menos cinco) menos dos multiplicar por (x más uno) es igual a cero
- (x-1)2*(x-5)-6-9*(x-5)-2*(x+1)=0
- x-12*x-5-6-9*x-5-2*x+1=0
- (x-1)²*(x-5)-6-9*(x-5)-2*(x+1)=0
- (x-1) en el grado 2*(x-5)-6-9*(x-5)-2*(x+1)=0
- (x-1)^2(x-5)-6-9(x-5)-2(x+1)=0
- (x-1)2(x-5)-6-9(x-5)-2(x+1)=0
- x-12x-5-6-9x-5-2x+1=0
- x-1^2x-5-6-9x-5-2x+1=0
- (x-1)^2*(x-5)-6-9*(x-5)-2*(x+1)=O
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Expresiones semejantes
- (x-1)^2*(x-5)-6+9*(x-5)-2*(x+1)=0
- (x-1)^2*(x+5)-6-9*(x-5)-2*(x+1)=0
- (x-1)^2*(x-5)-6-9*(x+5)-2*(x+1)=0
- (x+1)^2*(x-5)-6-9*(x-5)-2*(x+1)=0
- (x-1)^2*(x-5)-6-9*(x-5)-2*(x-1)=0
- (x-1)^2*(x-5)-6-9*(x-5)+2*(x+1)=0
- (x-1)^2*(x-5)+6-9*(x-5)-2*(x+1)=0
(x-1)^2*(x-5)-6-9*(x-5)-2*(x+1)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 (x - 1) *(x - 5) - 6 - 9*(x - 5) - 2*(x + 1) = 0
$$- 2 \left(x + 1\right) + \left(- 9 \left(x - 5\right) + \left(\left(x - 5\right) \left(x - 1\right)^{2} - 6\right)\right) = 0$$
Respuesta rápida
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/ 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\
49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 ||
| ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /|
|\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|
7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /
x1 = - - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- + -----------------------------| - -----------------------------
3 3 6 \ 3 6 6 / 6
$$x_{1} = - \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6}\right)$$
/ 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\
49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 ||
| ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /|
|\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|
7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /
x2 = - - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- - -----------------------------| + -----------------------------
3 3 6 \ 3 6 6 / 6
$$x_{2} = \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3}\right)$$
___________________
3 / _____
7 49 \/ 89 + 12*I*\/ 762
x3 = - - ------------------------ - ----------------------
3 ___________________ 3
3 / _____
3*\/ 89 + 12*I*\/ 762
$$x_{3} = \frac{7}{3} - \frac{\sqrt[3]{89 + 12 \sqrt{762} i}}{3} - \frac{49}{3 \sqrt[3]{89 + 12 \sqrt{762} i}}$$
x3 = 7/3 - (89 + 12*sqrt(762)*i)^(1/3)/3 - 49/(3*(89 + 12*sqrt(762)*i)^(1/3))
Suma y producto de raíces
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suma
/ 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\ / 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\
49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 || 49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 ||
| ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| | ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /| |3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /| ___________________
|\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------| |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------| 3 / _____
7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / 7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / 7 49 \/ 89 + 12*I*\/ 762
- - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- + -----------------------------| - ----------------------------- + - - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- - -----------------------------| + ----------------------------- + - - ------------------------ - ----------------------
3 3 6 \ 3 6 6 / 6 3 3 6 \ 3 6 6 / 6 3 ___________________ 3
3 / _____
3*\/ 89 + 12*I*\/ 762
$$\left(\frac{7}{3} - \frac{\sqrt[3]{89 + 12 \sqrt{762} i}}{3} - \frac{49}{3 \sqrt[3]{89 + 12 \sqrt{762} i}}\right) + \left(\left(\frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3}\right)\right) + \left(- \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / 1 \ / / _____\\ / / _____\\\
49*re|--------------------------------------| 49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 |||
| ___________________ / ___\| | ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| | | ___________________ / ___\| |atan|----------|| |atan|----------|||
|3 / _____ | 1 I*\/ 3 || |3 / _____ | 1 I*\/ 3 || ___________________ | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /||
|\/ 89 + 12*I*\/ 762 *|- - + -------|| |\/ 89 + 12*I*\/ 762 *|- - - -------|| 3 / _____ 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| | |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------||
49 \ \ 2 2 // \ \ 2 2 // \/ 89 + 12*I*\/ 762 \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| | \ \ 2 2 // \ 3 / \ 3 /|
7 - ------------------------ - --------------------------------------------- - --------------------------------------------- - ---------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- - -----------------------------| + I*|- --------------------------------------------- + ----------------------- + -----------------------------|
___________________ 3 3 3 3 \ 3 6 6 / \ 3 6 6 /
3 / _____
3*\/ 89 + 12*I*\/ 762
$$- \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{3} + 7 - \frac{\sqrt[3]{89 + 12 \sqrt{762} i}}{3} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6}\right) + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3}\right) - \frac{49}{3 \sqrt[3]{89 + 12 \sqrt{762} i}}$$
producto
/ / 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\\ / / 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\\
| 49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 ||| | 49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 |||
| | ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||| | | ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------|||
| |3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /|| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /|| / ___________________\
| |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|| | 3 / _____ |
|7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /| |7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /| |7 49 \/ 89 + 12*I*\/ 762 |
|- - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- + -----------------------------| - -----------------------------|*|- - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- - -----------------------------| + -----------------------------|*|- - ------------------------ - ----------------------|
\3 3 6 \ 3 6 6 / 6 / \3 3 6 \ 3 6 6 / 6 / |3 ___________________ 3 |
| 3 / _____ |
\ 3*\/ 89 + 12*I*\/ 762 /
$$\left(- \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6}\right)\right) \left(\frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3}\right)\right) \left(\frac{7}{3} - \frac{\sqrt[3]{89 + 12 \sqrt{762} i}}{3} - \frac{49}{3 \sqrt[3]{89 + 12 \sqrt{762} i}}\right)$$
=
/ / / _____\\ / / _____\\\
| | |12*\/ 762 || | |12*\/ 762 |||
/ ___________________ / ___________________\\ | |atan|----------|| |2*atan|----------|||
| 3 / _____ | 3 / _____ || | | \ 89 /| | \ 89 /||
-98*\49 - \/ 89 + 12*I*\/ 762 *\7 - \/ 89 + 12*I*\/ 762 //*|cos|----------------| + cos|------------------||
\ \ 3 / \ 3 //
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___________________
3 / _____
27*\/ 89 + 12*I*\/ 762
$$- \frac{98 \left(49 - \left(7 - \sqrt[3]{89 + 12 \sqrt{762} i}\right) \sqrt[3]{89 + 12 \sqrt{762} i}\right) \left(\cos{\left(\frac{2 \operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}\right)}{27 \sqrt[3]{89 + 12 \sqrt{762} i}}$$
-98*(49 - (89 + 12*i*sqrt(762))^(1/3)*(7 - (89 + 12*i*sqrt(762))^(1/3)))*(cos(atan(12*sqrt(762)/89)/3) + cos(2*atan(12*sqrt(762)/89)/3))/(27*(89 + 12*i*sqrt(762))^(1/3))
Respuesta numérica
[src]
x1 = 2.74111291847392
x2 = -1.89654952813192
x3 = 6.155436609658
x3 = 6.155436609658