Sr Examen
Otras calculadoras
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¿Cómo usar?
- La ecuación:
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Ecuación 9-7(x+3)=5-6x
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Ecuación 2x-4=8+2x
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Ecuación 2,4(x+0,98)=4,08
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Ecuación 7x=-30+2x
- Expresar {x} en función de y en la ecuación:
- 4*x+8*y=7
- -1*x+4*y=-10
- -16*x+10*y=-11
- 15*x+12*y=-19
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Expresiones idénticas
- sqrt(dos *x-y- tres)+sqrt(dos *y-x+ tres)=sqrt(tres -x-y)
- raíz cuadrada de (2 multiplicar por x menos y menos 3) más raíz cuadrada de (2 multiplicar por y menos x más 3) es igual a raíz cuadrada de (3 menos x menos y)
- raíz cuadrada de (dos multiplicar por x menos y menos tres) más raíz cuadrada de (dos multiplicar por y menos x más tres) es igual a raíz cuadrada de (tres menos x menos y)
- √(2*x-y-3)+√(2*y-x+3)=√(3-x-y)
- sqrt(2x-y-3)+sqrt(2y-x+3)=sqrt(3-x-y)
- sqrt2x-y-3+sqrt2y-x+3=sqrt3-x-y
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Expresiones semejantes
- sqrt(2*x-y-3)-sqrt(2*y-x+3)=sqrt(3-x-y)
- sqrt(2*x-y-3)+sqrt(2*y-x+3)=sqrt(3+x-y)
- sqrt(2*x+y-3)+sqrt(2*y-x+3)=sqrt(3-x-y)
- sqrt(2*x-y+3)+sqrt(2*y-x+3)=sqrt(3-x-y)
- sqrt(2*x-y-3)+sqrt(2*y-x+3)=sqrt(3-x+y)
- sqrt(2*x-y-3)+sqrt(2*y+x+3)=sqrt(3-x-y)
- sqrt(2*x-y-3)+sqrt(2*y-x-3)=sqrt(3-x-y)
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x+2)-sqrt(x-6)=2
- sqrt(4+2x−x^2)=x−2.
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(2*cot(x))-1=0
- Raíz cuadrada sqrt
- sqrt(x+2)-sqrt(x-6)=2
- sqrt(4+2x−x^2)=x−2.
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(2*cot(x))-1=0
- Raíz cuadrada sqrt
- sqrt(x+2)-sqrt(x-6)=2
- sqrt(4+2x−x^2)=x−2.
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(2*cot(x))-1=0
sqrt(2*x-y-3)+sqrt(2*y-x+3)=sqrt(3-x-y) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
_____________ _____________ ___________ \/ 2*x - y - 3 + \/ 2*y - x + 3 = \/ 3 - x - y
$$\sqrt{\left(- x + 2 y\right) + 3} + \sqrt{\left(2 x - y\right) - 3} = \sqrt{- y + \left(3 - x\right)}$$
Gráfica
Respuesta rápida
[src]
/ _______________________________________________ \ _______________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|
| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *sin|----------------------------------------------|| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *cos|----------------------------------------------|
re(y) |im(y) \ 2 /| \ 2 /
x1 = 2 + ----- + I*|----- - -------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------
2 \ 2 2 / 2
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(y\right)}}{2} + 2$$
/ _______________________________________________ \ _______________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|
| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *sin|----------------------------------------------|| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *cos|----------------------------------------------|
re(y) |im(y) \ 2 /| \ 2 /
x2 = 2 + ----- + I*|----- + -------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------
2 \ 2 2 / 2
$$x_{2} = i \left(\frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(y\right)}}{2} + 2$$
x2 = i*(((-3*re(y)^2 + 3*im(y)^2 + 1)^2 + 36*re(y)^2*im(y)^2)^(1/4)*sin(atan2(-6*re(y)*im(y, -3*re(y)^2 + 3*im(y)^2 + 1)/2)/2 + im(y)/2) + ((-3*re(y)^2 + 3*im(y)^2 + 1)^2 + 36*re(y)^2*im(y)^2)^(1/4)*cos(atan2(-6*re(y)*im(y), -3*re(y)^2 + 3*im(y)^2 + 1)/2)/2 + re(y)/2 + 2)
Suma y producto de raíces
[src]
suma
/ _______________________________________________ \ _______________________________________________ / _______________________________________________ \ _______________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/| | 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|
| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *sin|----------------------------------------------|| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *cos|----------------------------------------------| | \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *sin|----------------------------------------------|| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *cos|----------------------------------------------|
re(y) |im(y) \ 2 /| \ 2 / re(y) |im(y) \ 2 /| \ 2 /
2 + ----- + I*|----- - -------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------- + 2 + ----- + I*|----- + -------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------
2 \ 2 2 / 2 2 \ 2 2 / 2
$$\left(i \left(- \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(y\right)}}{2} + 2\right) + \left(i \left(\frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(y\right)}}{2} + 2\right)$$
=
/ _______________________________________________ \ / _______________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/||
| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *sin|----------------------------------------------|| | \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *sin|----------------------------------------------||
|im(y) \ 2 /| |im(y) \ 2 /|
4 + I*|----- + -------------------------------------------------------------------------------------------------------| + I*|----- - -------------------------------------------------------------------------------------------------------| + re(y)
\ 2 2 / \ 2 2 /
$$i \left(- \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(y\right)}}{2}\right) + i \left(\frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \operatorname{re}{\left(y\right)} + 4$$
producto
/ / _______________________________________________ \ _______________________________________________ \ / / _______________________________________________ \ _______________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| | | 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| 4 / / 2 2 \ 2 2 |atan2\-6*im(y)*re(y), 1 - 3*re (y) + 3*im (y)/|| | | \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *sin|----------------------------------------------|| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *cos|----------------------------------------------|| | | \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *sin|----------------------------------------------|| \/ \1 - 3*re (y) + 3*im (y)/ + 36*im (y)*re (y) *cos|----------------------------------------------|| | re(y) |im(y) \ 2 /| \ 2 /| | re(y) |im(y) \ 2 /| \ 2 /| |2 + ----- + I*|----- - -------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------|*|2 + ----- + I*|----- + -------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------| \ 2 \ 2 2 / 2 / \ 2 \ 2 2 / 2 /
$$\left(i \left(- \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(y\right)}}{2} + 2\right) \left(i \left(\frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(y\right)}}{2} + 2\right)$$
=
15 2 2 -- + re (y) - im (y) + 2*re(y) + 2*I*im(y) + 2*I*im(y)*re(y) 4
$$\left(\operatorname{re}{\left(y\right)}\right)^{2} + 2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2 i \operatorname{im}{\left(y\right)} + \frac{15}{4}$$
15/4 + re(y)^2 - im(y)^2 + 2*re(y) + 2*i*im(y) + 2*i*im(y)*re(y)