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- La ecuación:
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Ecuación (x+9)^2=36*x
-
Ecuación a+120=2000/5
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Ecuación -x/11+x=50/11
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Ecuación x^2+7x+6=0
- Expresar {x} en función de y en la ecuación:
- 12*x+8*y=18
- 8*x+6*y=20
- -2*x+18*y=13
- -11*x-1*y=15
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Expresiones idénticas
- cosx- dos |cosx|=y
- coseno de x menos 2 módulo de coseno de x| es igual a y
- coseno de x menos dos módulo de coseno de x| es igual a y
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Expresiones semejantes
- cosx+2|cosx|=y
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Expresiones con funciones
- Módulo |
- |x|=3,2
- |x+3|+|x-2|=7
- |x|=5,6
- |x|=2,8
- |x|+3=5
cosx-2|cosx|=y la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
cos(x) - 2*|cos(x)| = y
$$\cos{\left(x \right)} - 2 \left|{\cos{\left(x \right)}}\right| = y$$
Gráfica
Respuesta rápida
[src]
//-acos(-y) + 2*pi for y <= 0\ //-acos(-y) + 2*pi for y <= 0\
x1 = I*im|< | + re|< |
\\ nan otherwise / \\ nan otherwise /
$$x_{1} = \operatorname{re}{\left(\begin{cases} - \operatorname{acos}{\left(- y \right)} + 2 \pi & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \operatorname{acos}{\left(- y \right)} + 2 \pi & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// /y\ \ // /y\ \
||- acos|-| + 2*pi for y < 0| ||- acos|-| + 2*pi for y < 0|
x2 = I*im|< \3/ | + re|< \3/ |
|| | || |
\\ nan otherwise/ \\ nan otherwise/
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \operatorname{acos}{\left(\frac{y}{3} \right)} + 2 \pi & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \operatorname{acos}{\left(\frac{y}{3} \right)} + 2 \pi & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
//acos(-y) for y <= 0\ //acos(-y) for y <= 0\
x3 = I*im|< | + re|< |
\\ nan otherwise / \\ nan otherwise /
$$x_{3} = \operatorname{re}{\left(\begin{cases} \operatorname{acos}{\left(- y \right)} & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \operatorname{acos}{\left(- y \right)} & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// /y\ \ // /y\ \
||acos|-| for y < 0| ||acos|-| for y < 0|
x4 = I*im|< \3/ | + re|< \3/ |
|| | || |
\\ nan otherwise/ \\ nan otherwise/
$$x_{4} = \operatorname{re}{\left(\begin{cases} \operatorname{acos}{\left(\frac{y}{3} \right)} & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \operatorname{acos}{\left(\frac{y}{3} \right)} & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((acos(y/3, y < 0), (nan, True))) + i*im(Piecewise((acos(y/3), y < 0), (nan, True))))
Suma y producto de raíces
[src]
suma
// /y\ \ // /y\ \ // /y\ \ // /y\ \
//-acos(-y) + 2*pi for y <= 0\ //-acos(-y) + 2*pi for y <= 0\ ||- acos|-| + 2*pi for y < 0| ||- acos|-| + 2*pi for y < 0| //acos(-y) for y <= 0\ //acos(-y) for y <= 0\ ||acos|-| for y < 0| ||acos|-| for y < 0|
I*im|< | + re|< | + I*im|< \3/ | + re|< \3/ | + I*im|< | + re|< | + I*im|< \3/ | + re|< \3/ |
\\ nan otherwise / \\ nan otherwise / || | || | \\ nan otherwise / \\ nan otherwise / || | || |
\\ nan otherwise/ \\ nan otherwise/ \\ nan otherwise/ \\ nan otherwise/
$$\left(\left(\left(\operatorname{re}{\left(\begin{cases} - \operatorname{acos}{\left(- y \right)} + 2 \pi & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \operatorname{acos}{\left(- y \right)} + 2 \pi & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} - \operatorname{acos}{\left(\frac{y}{3} \right)} + 2 \pi & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \operatorname{acos}{\left(\frac{y}{3} \right)} + 2 \pi & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} \operatorname{acos}{\left(- y \right)} & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \operatorname{acos}{\left(- y \right)} & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} \operatorname{acos}{\left(\frac{y}{3} \right)} & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \operatorname{acos}{\left(\frac{y}{3} \right)} & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
// /y\ \ // /y\ \ // /y\ \ // /y\ \
//-acos(-y) + 2*pi for y <= 0\ ||- acos|-| + 2*pi for y < 0| //acos(-y) for y <= 0\ ||acos|-| for y < 0| //-acos(-y) + 2*pi for y <= 0\ ||- acos|-| + 2*pi for y < 0| //acos(-y) for y <= 0\ ||acos|-| for y < 0|
I*im|< | + I*im|< \3/ | + I*im|< | + I*im|< \3/ | + re|< | + re|< \3/ | + re|< | + re|< \3/ |
\\ nan otherwise / || | \\ nan otherwise / || | \\ nan otherwise / || | \\ nan otherwise / || |
\\ nan otherwise/ \\ nan otherwise/ \\ nan otherwise/ \\ nan otherwise/
$$\operatorname{re}{\left(\begin{cases} - \operatorname{acos}{\left(- y \right)} + 2 \pi & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - \operatorname{acos}{\left(\frac{y}{3} \right)} + 2 \pi & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \operatorname{acos}{\left(- y \right)} & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \operatorname{acos}{\left(\frac{y}{3} \right)} & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \operatorname{acos}{\left(- y \right)} + 2 \pi & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \operatorname{acos}{\left(\frac{y}{3} \right)} + 2 \pi & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \operatorname{acos}{\left(- y \right)} & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \operatorname{acos}{\left(\frac{y}{3} \right)} & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
producto
/ // /y\ \ // /y\ \\ / // /y\ \ // /y\ \\
/ //-acos(-y) + 2*pi for y <= 0\ //-acos(-y) + 2*pi for y <= 0\\ | ||- acos|-| + 2*pi for y < 0| ||- acos|-| + 2*pi for y < 0|| / //acos(-y) for y <= 0\ //acos(-y) for y <= 0\\ | ||acos|-| for y < 0| ||acos|-| for y < 0||
|I*im|< | + re|< ||*|I*im|< \3/ | + re|< \3/ ||*|I*im|< | + re|< ||*|I*im|< \3/ | + re|< \3/ ||
\ \\ nan otherwise / \\ nan otherwise // | || | || || \ \\ nan otherwise / \\ nan otherwise // | || | || ||
\ \\ nan otherwise/ \\ nan otherwise// \ \\ nan otherwise/ \\ nan otherwise//
$$\left(\operatorname{re}{\left(\begin{cases} - \operatorname{acos}{\left(- y \right)} + 2 \pi & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \operatorname{acos}{\left(- y \right)} + 2 \pi & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - \operatorname{acos}{\left(\frac{y}{3} \right)} + 2 \pi & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \operatorname{acos}{\left(\frac{y}{3} \right)} + 2 \pi & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \operatorname{acos}{\left(- y \right)} & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \operatorname{acos}{\left(- y \right)} & \text{for}\: y \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \operatorname{acos}{\left(\frac{y}{3} \right)} & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \operatorname{acos}{\left(\frac{y}{3} \right)} & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
/ / / /y\\ / /y\\\ / / /y\\ / /y\\\ |(I*im(acos(-y)) + re(acos(-y)))*|I*im|acos|-|| + re|acos|-|||*(-2*pi + I*im(acos(-y)) + re(acos(-y)))*|-2*pi + I*im|acos|-|| + re|acos|-||| for y < 0 < \ \ \3// \ \3/// \ \ \3// \ \3/// | \ nan otherwise
$$\begin{cases} \left(\operatorname{re}{\left(\operatorname{acos}{\left(- y \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- y \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{y}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{y}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- y \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- y \right)}\right)} - 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{y}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{y}{3} \right)}\right)} - 2 \pi\right) & \text{for}\: y < 0 \\\text{NaN} & \text{otherwise} \end{cases}$$
Piecewise(((i*im(acos(-y)) + re(acos(-y)))*(i*im(acos(y/3)) + re(acos(y/3)))*(-2*pi + i*im(acos(-y)) + re(acos(-y)))*(-2*pi + i*im(acos(y/3)) + re(acos(y/3))), y < 0), (nan, True))