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La ecuación:
Ecuación 12-y+2=0
Ecuación 5*x^2+9*x=0
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Ecuación (1/6)^(x+8)=6^x
Expresar {x} en función de y en la ecuación:
-4*x+4*y=-9
8*x-9*y=-1
-14*x+19*y=-3
-4*x-4*y=19
Expresiones idénticas
sqrt(a-2xy)=x-y+ siete
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raíz cuadrada de (a menos 2xy) es igual a x menos y más siete
√(a-2xy)=x-y+7
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Expresiones semejantes
sqrt(a+2xy)=x-y+7
sqrt(a-2xy)=x-y-7
sqrt(a-2xy)=x+y+7
Expresiones con funciones
Raíz cuadrada sqrt
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sqrt(r)=-r

sqrt(a-2xy)=x-y+7 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

  ___________            
\/ a - 2*x*y  = x - y + 7

\sqrt{a - 2 x y} = \left(x - y\right) + 7

Simplificar

Solución detallada

Tenemos la ecuación

\sqrt{a - 2 x y} = \left(x - y\right) + 7

\sqrt{a - 2 x y} = x - y + 7

Elevemos las dos partes de la ecuación a la potencia 2

a - 2 x y = \left(x - y + 7\right)^{2}

a - 2 x y = x^{2} - 2 x y + 14 x + y^{2} - 14 y + 49

Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo

a - x^{2} - 14 x - y^{2} + 14 y - 49 = 0

Es la ecuación de la forma

a*x^2 + b*x + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:

x_{1} = \frac{\sqrt{D} - b}{2 a}

x_{2} = \frac{- \sqrt{D} - b}{2 a}

donde D = b^2 - 4*a*c es el discriminante.
Como

a = -1

b = -14

c = a - y^{2} + 14 y - 49

, entonces

D = b^2 - 4 * a * c =

(-14)^2 - 4 * (-1) * (-49 + a - y^2 + 14*y) = -4*y^2 + 4*a + 56*y

La ecuación tiene dos raíces.

x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

x_{1} = - \frac{\sqrt{4 a - 4 y^{2} + 56 y}}{2} - 7

x_{2} = \frac{\sqrt{4 a - 4 y^{2} + 56 y}}{2} - 7

Gráfica

Respuesta rápida [src]

              _____________________________________________________________________________                                                                                          _____________________________________________________________________________                                                                                 
             /                                                                           2     /     /                                    2        2                      \\        /                                                                           2     /     /                                    2        2                      \\
          4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|
x1 = -7 - \/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *cos|---------------------------------------------------------------------------| - I*\/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *sin|---------------------------------------------------------------------------|
                                                                                               \                                     2                                     /                                                                                          \                                     2                                     /

x_{1} = - i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - 7

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             /                                                                           2     /     /                                    2        2                      \\        /                                                                           2     /     /                                    2        2                      \\
          4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|
x2 = -7 + \/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *cos|---------------------------------------------------------------------------| + I*\/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *sin|---------------------------------------------------------------------------|
                                                                                               \                                     2                                     /                                                                                          \                                     2                                     /

x_{2} = i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - 7

x2 = i*((-2*re(y)*im(y) + im(a) + 14*im(y))^2 + (re(a) - re(y)^2 + 14*re(y) + im(y)^2)^2)^(1/4)*sin(atan2(-2*re(y)*im(y) + im(a) + 14*im(y, re(a) - re(y)^2 + 14*re(y) + im(y)^2)/2) + ((-2*re(y)*im(y) + im(a) + 14*im(y))^2 + (re(a) - re(y)^2 + 14*re(y) + im(y)^2)^2)^(1/4)*cos(atan2(-2*re(y)*im(y) + im(a) + 14*im(y), re(a) - re(y)^2 + 14*re(y) + im(y)^2)/2) - 7)

Suma y producto de raíces [src]

suma

         _____________________________________________________________________________                                                                                          _____________________________________________________________________________                                                                                             _____________________________________________________________________________                                                                                          _____________________________________________________________________________                                                                                 
        /                                                                           2     /     /                                    2        2                      \\        /                                                                           2     /     /                                    2        2                      \\           /                                                                           2     /     /                                    2        2                      \\        /                                                                           2     /     /                                    2        2                      \\
     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|        4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|
-7 - \/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *cos|---------------------------------------------------------------------------| - I*\/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *sin|---------------------------------------------------------------------------| + -7 + \/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *cos|---------------------------------------------------------------------------| + I*\/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *sin|---------------------------------------------------------------------------|
                                                                                          \                                     2                                     /                                                                                          \                                     2                                     /                                                                                             \                                     2                                     /                                                                                          \                                     2                                     /

\left(- i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - 7\right) + \left(i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - 7\right)

-14

-14

producto

/         _____________________________________________________________________________                                                                                          _____________________________________________________________________________                                                                                 \ /         _____________________________________________________________________________                                                                                          _____________________________________________________________________________                                                                                 \
|        /                                                                           2     /     /                                    2        2                      \\        /                                                                           2     /     /                                    2        2                      \\| |        /                                                                           2     /     /                                    2        2                      \\        /                                                                           2     /     /                                    2        2                      \\|
|     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|| |     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/|     4 /                                    2   /  2        2                      \      |atan2\14*im(y) - 2*im(y)*re(y) + im(a), im (y) - re (y) + 14*re(y) + re(a)/||
|-7 - \/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *cos|---------------------------------------------------------------------------| - I*\/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *sin|---------------------------------------------------------------------------||*|-7 + \/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *cos|---------------------------------------------------------------------------| + I*\/   (14*im(y) - 2*im(y)*re(y) + im(a))  + \im (y) - re (y) + 14*re(y) + re(a)/  *sin|---------------------------------------------------------------------------||
\                                                                                          \                                     2                                     /                                                                                          \                                     2                                     // \                                                                                          \                                     2                                     /                                                                                          \                                     2                                     //

\left(- i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - 7\right) \left(i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(y\right)},\operatorname{re}{\left(a\right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + 14 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - 7\right)

       2        2                                                               
49 + re (y) - im (y) - re(a) - 14*re(y) - I*im(a) - 14*I*im(y) + 2*I*im(y)*re(y)

- \operatorname{re}{\left(a\right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + 2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 14 \operatorname{re}{\left(y\right)} - i \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 14 i \operatorname{im}{\left(y\right)} + 49

49 + re(y)^2 - im(y)^2 - re(a) - 14*re(y) - i*im(a) - 14*i*im(y) + 2*i*im(y)*re(y)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

sqrt(a-2xy)=x-y+7 la ecuación

Solución numérica:

Solución