Sr Examen
Otras calculadoras
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- La ecuación:
- Ecuación x^2-49=0
-
Ecuación 1-x/2=x/3
-
Ecuación 3*x^2-9=0
-
Ecuación -8x-17=3x-105
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- -19*x+14*y=20
- 5*x-14*y=-15
-
Expresiones idénticas
- (tres x+ siete)(y-3)=(dos +y)(cinco +y)+ cuarenta y cinco
- (3x más 7)(y menos 3) es igual a (2 más y)(5 más y) más 45
- (tres x más siete)(y menos 3) es igual a (dos más y)(cinco más y) más cuarenta y cinco
- 3x+7y-3=2+y5+y+45
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Expresiones semejantes
- (3x+7)(y-3)=(2+y)(5+y)-45
- (3x+7)(y-3)=(2+y)(5-y)+45
- (y-7)*(y-3)=(2+y)*(5+y)+45
- (3x+7)(y-3)=(2-y)(5+y)+45
- (3x-7)(y-3)=(2+y)(5+y)+45
- (3x+7)(y+3)=(2+y)(5+y)+45
(3x+7)(y-3)=(2+y)(5+y)+45 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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(3*x + 7)*(y - 3) = (2 + y)*(5 + y) + 45
$$\left(3 x + 7\right) \left(y - 3\right) = \left(y + 2\right) \left(y + 5\right) + 45$$
Solución detallada
Tenemos la ecuación:
Abrimos la expresión:
Reducimos, obtenemos:
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$3 x y - 9 x - y^{2} = 76$$
Dividamos ambos miembros de la ecuación en (-y^2 - 9*x + 3*x*y)/x
Obtenemos la respuesta: x = (76 + y^2)/(3*(-3 + y))
(3*x+7)*(y-3) = (2+y)*(5+y)+45
Abrimos la expresión:
-21 - 9*x + 7*y + 3*x*y = (2+y)*(5+y)+45
(3*x+7)*(y-3) = 10 + y^2 + 7*y + 45
Reducimos, obtenemos:
-76 - y^2 - 9*x + 3*x*y = 0
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$3 x y - 9 x - y^{2} = 76$$
Dividamos ambos miembros de la ecuación en (-y^2 - 9*x + 3*x*y)/x
x = 76 / ((-y^2 - 9*x + 3*x*y)/x)
Obtenemos la respuesta: x = (76 + y^2)/(3*(-3 + y))
Gráfica
Respuesta rápida
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/ / 2 2 \ \ / 2 2 \ 2
| \76 + re (y) - im (y)/*im(y) 2*(-3 + re(y))*im(y)*re(y)| (-3 + re(y))*\76 + re (y) - im (y)/ 2*im (y)*re(y)
x1 = I*|- ---------------------------- + --------------------------| + ----------------------------------- + --------------------------
| / 2 2 \ / 2 2 \| / 2 2 \ / 2 2 \
\ 3*\(-3 + re(y)) + im (y)/ 3*\(-3 + re(y)) + im (y)// 3*\(-3 + re(y)) + im (y)/ 3*\(-3 + re(y)) + im (y)/
$$x_{1} = i \left(\frac{2 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right) \operatorname{im}{\left(y\right)}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right)}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} + \frac{2 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$
x1 = i*(2*(re(y) - 3)*re(y)*im(y)/(3*((re(y) - 3)^2 + im(y)^2)) - (re(y)^2 - im(y)^2 + 76)*im(y)/(3*((re(y) - 3)^2 + im(y)^2))) + (re(y) - 3)*(re(y)^2 - im(y)^2 + 76)/(3*((re(y) - 3)^2 + im(y)^2)) + 2*re(y)*im(y)^2/(3*((re(y) - 3)^2 + im(y)^2))
Suma y producto de raíces
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suma
/ / 2 2 \ \ / 2 2 \ 2 | \76 + re (y) - im (y)/*im(y) 2*(-3 + re(y))*im(y)*re(y)| (-3 + re(y))*\76 + re (y) - im (y)/ 2*im (y)*re(y) I*|- ---------------------------- + --------------------------| + ----------------------------------- + -------------------------- | / 2 2 \ / 2 2 \| / 2 2 \ / 2 2 \ \ 3*\(-3 + re(y)) + im (y)/ 3*\(-3 + re(y)) + im (y)// 3*\(-3 + re(y)) + im (y)/ 3*\(-3 + re(y)) + im (y)/
$$i \left(\frac{2 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right) \operatorname{im}{\left(y\right)}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right)}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} + \frac{2 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$
=
/ / 2 2 \ \ / 2 2 \ 2 | \76 + re (y) - im (y)/*im(y) 2*(-3 + re(y))*im(y)*re(y)| (-3 + re(y))*\76 + re (y) - im (y)/ 2*im (y)*re(y) I*|- ---------------------------- + --------------------------| + ----------------------------------- + -------------------------- | / 2 2 \ / 2 2 \| / 2 2 \ / 2 2 \ \ 3*\(-3 + re(y)) + im (y)/ 3*\(-3 + re(y)) + im (y)// 3*\(-3 + re(y)) + im (y)/ 3*\(-3 + re(y)) + im (y)/
$$i \left(\frac{2 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right) \operatorname{im}{\left(y\right)}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right)}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} + \frac{2 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$
producto
/ / 2 2 \ \ / 2 2 \ 2 | \76 + re (y) - im (y)/*im(y) 2*(-3 + re(y))*im(y)*re(y)| (-3 + re(y))*\76 + re (y) - im (y)/ 2*im (y)*re(y) I*|- ---------------------------- + --------------------------| + ----------------------------------- + -------------------------- | / 2 2 \ / 2 2 \| / 2 2 \ / 2 2 \ \ 3*\(-3 + re(y)) + im (y)/ 3*\(-3 + re(y)) + im (y)// 3*\(-3 + re(y)) + im (y)/ 3*\(-3 + re(y)) + im (y)/
$$i \left(\frac{2 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right) \operatorname{im}{\left(y\right)}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right)}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} + \frac{2 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$
=
/ 2 2 \ 2 / 2 2 \
(-3 + re(y))*\76 + re (y) - im (y)/ + 2*im (y)*re(y) + I*\-76 + im (y) - re (y) + 2*(-3 + re(y))*re(y)/*im(y)
-------------------------------------------------------------------------------------------------------------
/ 2 2 \
3*\(-3 + re(y)) + im (y)/
$$\frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 76\right) + i \left(2 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{re}{\left(y\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 76\right) \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{3 \left(\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$
((-3 + re(y))*(76 + re(y)^2 - im(y)^2) + 2*im(y)^2*re(y) + i*(-76 + im(y)^2 - re(y)^2 + 2*(-3 + re(y))*re(y))*im(y))/(3*((-3 + re(y))^2 + im(y)^2))