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- La ecuación:
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Ecuación 6*x^2+x-7=0
- Ecuación z^5+32=0
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Ecuación 2-5(3+2x)=17
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Ecuación (6*x+8)/2+5=5*x/3
- Expresar {x} en función de y en la ecuación:
- -8*x+3*y=-4
- 16*x-17*y=-15
- -10*x-12*y=-10
- 4*x+12*y=-11
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Expresiones idénticas
- sqrt(dos *a*y*(b+a)-a^(dos))-c-a= cero
- raíz cuadrada de (2 multiplicar por a multiplicar por y multiplicar por (b más a) menos a en el grado (2)) menos c menos a es igual a 0
- raíz cuadrada de (dos multiplicar por a multiplicar por y multiplicar por (b más a) menos a en el grado (dos)) menos c menos a es igual a cero
- √(2*a*y*(b+a)-a^(2))-c-a=0
- sqrt(2*a*y*(b+a)-a(2))-c-a=0
- sqrt2*a*y*b+a-a2-c-a=0
- sqrt(2ay(b+a)-a^(2))-c-a=0
- sqrt(2ay(b+a)-a(2))-c-a=0
- sqrt2ayb+a-a2-c-a=0
- sqrt2ayb+a-a^2-c-a=0
- sqrt(2*a*y*(b+a)-a^(2))-c-a=O
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Expresiones semejantes
- sqrt(2*a*y*(b+a)+a^(2))-c-a=0
- sqrt(2*a*y*(b-a)-a^(2))-c-a=0
- sqrt(2*a*y*(b+a)-a^(2))-c+a=0
- sqrt(2*a*y*(b+a)-a^(2))+c-a=0
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(7-8×x+sqr(x))+sqrt(sqr(x)-8×x-5)=-sqr(x)+8×x+15
- sqrt((x)/(x-2))+sqrt((x-2)/(x))=5/2
- sqrt(7+3x)-sqrt(5-4x)+1=0
- sqrt((1-a)^10)=(1-a)^5
- Sqrt(x^2-1)*sqrt(y^2-1)=a^2-1
sqrt(2*a*y*(b+a)-a^(2))-c-a=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
____________________ / 2 \/ 2*a*y*(b + a) - a - c - a = 0
$$- a + \left(- c + \sqrt{- a^{2} + 2 a y \left(a + b\right)}\right) = 0$$
Gráfica
Respuesta rápida
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/ / 1 \ / 2 2 2 2 \ / 1 \\ / 2 2 2 2 \ / 1 \ / 1 \
|(2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*re|---------| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*im|---------|| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*re|---------| (2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*im|---------|
| \a*(a + b)/ \a*(a + b)/| \a*(a + b)/ \a*(a + b)/
y1 = I*|----------------------------------------------------------------- + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - -----------------------------------------------------------------
\ 2 2 / 2 2
$$y_{1} = i \left(\frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}$$
y1 = i*((2*(re(a) + re(c))*(im(a) + im(c)) + 2*re(a)*im(a))*re(1/(a*(a + b)))/2 + ((re(a) + re(c))^2 - (im(a) + im(c))^2 + re(a)^2 - im(a)^2)*im(1/(a*(a + b)))/2) - (2*(re(a) + re(c))*(im(a) + im(c)) + 2*re(a)*im(a))*im(1/(a*(a + b)))/2 + ((re(a) + re(c))^2 - (im(a) + im(c))^2 + re(a)^2 - im(a)^2)*re(1/(a*(a + b)))/2
Suma y producto de raíces
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suma
/ / 1 \ / 2 2 2 2 \ / 1 \\ / 2 2 2 2 \ / 1 \ / 1 \ |(2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*re|---------| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*im|---------|| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*re|---------| (2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*im|---------| | \a*(a + b)/ \a*(a + b)/| \a*(a + b)/ \a*(a + b)/ I*|----------------------------------------------------------------- + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - ----------------------------------------------------------------- \ 2 2 / 2 2
$$i \left(\frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}$$
=
/ / 1 \ / 2 2 2 2 \ / 1 \\ / 2 2 2 2 \ / 1 \ / 1 \ |(2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*re|---------| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*im|---------|| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*re|---------| (2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*im|---------| | \a*(a + b)/ \a*(a + b)/| \a*(a + b)/ \a*(a + b)/ I*|----------------------------------------------------------------- + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - ----------------------------------------------------------------- \ 2 2 / 2 2
$$i \left(\frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}$$
producto
/ / 1 \ / 2 2 2 2 \ / 1 \\ / 2 2 2 2 \ / 1 \ / 1 \ |(2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*re|---------| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*im|---------|| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*re|---------| (2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*im|---------| | \a*(a + b)/ \a*(a + b)/| \a*(a + b)/ \a*(a + b)/ I*|----------------------------------------------------------------- + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - ----------------------------------------------------------------- \ 2 2 / 2 2
$$i \left(\frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}$$
=
/ / 2 2 2 2 \ / 1 \\ / 2 2 2 2 \ / 1 \ | \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*im|---------|| \(re(a) + re(c)) + re (a) - (im(a) + im(c)) - im (a)/*re|---------| | / 1 \ \a*(a + b)/| \a*(a + b)/ / 1 \ I*|((im(a) + im(c))*(re(a) + re(c)) + im(a)*re(a))*re|---------| + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - ((im(a) + im(c))*(re(a) + re(c)) + im(a)*re(a))*im|---------| \ \a*(a + b)/ 2 / 2 \a*(a + b)/
$$i \left(\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}$$
i*(((im(a) + im(c))*(re(a) + re(c)) + im(a)*re(a))*re(1/(a*(a + b))) + ((re(a) + re(c))^2 + re(a)^2 - (im(a) + im(c))^2 - im(a)^2)*im(1/(a*(a + b)))/2) + ((re(a) + re(c))^2 + re(a)^2 - (im(a) + im(c))^2 - im(a)^2)*re(1/(a*(a + b)))/2 - ((im(a) + im(c))*(re(a) + re(c)) + im(a)*re(a))*im(1/(a*(a + b)))