Sr Examen
Otras calculadoras
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¿Cómo usar?
- La ecuación:
-
Ecuación (x-3)*(x+2)=0
-
Ecuación z^2-6*z+10=0
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Ecuación 4/(x-4)=-5
-
Ecuación (x-6)^2=-24*x
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- -14*x-12*y=5
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Expresiones idénticas
- sqrt(x- dos)+sqrt(y- dos)= dos
- raíz cuadrada de (x menos 2) más raíz cuadrada de (y menos 2) es igual a 2
- raíz cuadrada de (x menos dos) más raíz cuadrada de (y menos dos) es igual a dos
- √(x-2)+√(y-2)=2
- sqrtx-2+sqrty-2=2
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Expresiones semejantes
- sqrt(x-2)+sqrt(y+2)=2
- sqrt(x-2)-sqrt(y-2)=2
- sqrt(x+2)+sqrt(y-2)=2
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x)=1
- sqrt(x^2+9)=2*x-3
- sqrt(x)=-2
- sqrt(2-x)+sqrt(-x-1)=sqrt(-5*x-7)
- sqrt(5-x)=x-3
- Raíz cuadrada sqrt
- sqrt(x)=1
- sqrt(x^2+9)=2*x-3
- sqrt(x)=-2
- sqrt(2-x)+sqrt(-x-1)=sqrt(-5*x-7)
- sqrt(5-x)=x-3
sqrt(x-2)+sqrt(y-2)=2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
Suma y producto de raíces
[src]
suma
2
/ ________________________ \ ________________________ ________________________ / ________________________ \
| 4 / 2 2 /atan2(im(y), -2 + re(y))\| / 2 2 2/atan2(im(y), -2 + re(y))\ 4 / 2 2 | 4 / 2 2 /atan2(im(y), -2 + re(y))\| /atan2(im(y), -2 + re(y))\
2 + |-2 + \/ (-2 + re(y)) + im (y) *cos|------------------------|| - \/ (-2 + re(y)) + im (y) *sin |------------------------| + 2*I*\/ (-2 + re(y)) + im (y) *|-2 + \/ (-2 + re(y)) + im (y) *cos|------------------------||*sin|------------------------|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + 2$$
=
2
/ ________________________ \ ________________________ ________________________ / ________________________ \
| 4 / 2 2 /atan2(im(y), -2 + re(y))\| / 2 2 2/atan2(im(y), -2 + re(y))\ 4 / 2 2 | 4 / 2 2 /atan2(im(y), -2 + re(y))\| /atan2(im(y), -2 + re(y))\
2 + |-2 + \/ (-2 + re(y)) + im (y) *cos|------------------------|| - \/ (-2 + re(y)) + im (y) *sin |------------------------| + 2*I*\/ (-2 + re(y)) + im (y) *|-2 + \/ (-2 + re(y)) + im (y) *cos|------------------------||*sin|------------------------|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + 2$$
producto
2
/ ________________________ \ ________________________ ________________________ / ________________________ \
| 4 / 2 2 /atan2(im(y), -2 + re(y))\| / 2 2 2/atan2(im(y), -2 + re(y))\ 4 / 2 2 | 4 / 2 2 /atan2(im(y), -2 + re(y))\| /atan2(im(y), -2 + re(y))\
2 + |-2 + \/ (-2 + re(y)) + im (y) *cos|------------------------|| - \/ (-2 + re(y)) + im (y) *sin |------------------------| + 2*I*\/ (-2 + re(y)) + im (y) *|-2 + \/ (-2 + re(y)) + im (y) *cos|------------------------||*sin|------------------------|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + 2$$
=
_______________________________ _______________________________
/ 2 2 _______________________________ / 2 2 _______________________________
re(y) \/ 4 + im (y) + re (y) - 4*re(y) 4 / 2 2 /atan2(im(y), -2 + re(y))\ \/ 4 + im (y) + re (y) - 4*re(y) *re(y) 4 / 2 2 /atan2(im(y), -2 + re(y))\
5 + ----- + I*im(y) - ---------------------------------- - 4*\/ 4 + im (y) + re (y) - 4*re(y) *cos|------------------------| + ---------------------------------------- - 4*I*\/ 4 + im (y) + re (y) - 4*re(y) *sin|------------------------|
2 ________________________ \ 2 / ________________________ \ 2 /
/ 2 2 / 2 2
\/ (-2 + re(y)) + im (y) 2*\/ (-2 + re(y)) + im (y)
$$- 4 i \sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 4 \sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + \frac{\operatorname{re}{\left(y\right)}}{2} + i \operatorname{im}{\left(y\right)} + 5 + \frac{\sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4} \operatorname{re}{\left(y\right)}}{2 \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} - \frac{\sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4}}{\sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}}$$
5 + re(y)/2 + i*im(y) - sqrt(4 + im(y)^2 + re(y)^2 - 4*re(y))/sqrt((-2 + re(y))^2 + im(y)^2) - 4*(4 + im(y)^2 + re(y)^2 - 4*re(y))^(1/4)*cos(atan2(im(y), -2 + re(y))/2) + sqrt(4 + im(y)^2 + re(y)^2 - 4*re(y))*re(y)/(2*sqrt((-2 + re(y))^2 + im(y)^2)) - 4*i*(4 + im(y)^2 + re(y)^2 - 4*re(y))^(1/4)*sin(atan2(im(y), -2 + re(y))/2)
Respuesta rápida
[src]
2
/ ________________________ \ ________________________ ________________________ / ________________________ \
| 4 / 2 2 /atan2(im(y), -2 + re(y))\| / 2 2 2/atan2(im(y), -2 + re(y))\ 4 / 2 2 | 4 / 2 2 /atan2(im(y), -2 + re(y))\| /atan2(im(y), -2 + re(y))\
x1 = 2 + |-2 + \/ (-2 + re(y)) + im (y) *cos|------------------------|| - \/ (-2 + re(y)) + im (y) *sin |------------------------| + 2*I*\/ (-2 + re(y)) + im (y) *|-2 + \/ (-2 + re(y)) + im (y) *cos|------------------------||*sin|------------------------|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$x_{1} = \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + 2$$
x1 = (((re(y) - 2)^2 + im(y)^2)^(1/4)*cos(atan2(im(y, re(y) - 2)/2) - 2)^2 + 2*i*(((re(y) - 2)^2 + im(y)^2)^(1/4)*cos(atan2(im(y), re(y) - 2)/2) - 2)*((re(y) - 2)^2 + im(y)^2)^(1/4)*sin(atan2(im(y), re(y) - 2)/2) - sqrt((re(y) - 2)^2 + im(y)^2)*sin(atan2(im(y), re(y) - 2)/2)^2 + 2)