Sr Examen

Otras calculadoras

Solución de sistemas de ecuaciones/ yx+2y=2; y^2+=x

yx+2y=2; y^2+=x

v

Gráfico:

interior superior

interior superior

Solución

Ha introducido [src] 
y*x + 2*y = 2
xy+2y=2x y + 2 y = 2 
 2    
y  = x
y2=xy^{2} = x 
y^2 = x
Respuesta rápida
x1=((−12−3i2)1+10593−23(−12−3i2)1+10593)2x_{1} = \left(\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + \frac{\sqrt{105}}{9}} - \frac{2}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + \frac{\sqrt{105}}{9}}}\right)^{2}
=
323(−833+(1+3i)2(9+105)23)236(1+3i)2(9+105)23\frac{3^{\frac{2}{3}} \left(- 8 \sqrt[3]{3} + \left(1 + \sqrt{3} i\right)^{2} \left(9 + \sqrt{105}\right)^{\frac{2}{3}}\right)^{2}}{36 \left(1 + \sqrt{3} i\right)^{2} \left(9 + \sqrt{105}\right)^{\frac{2}{3}}}
=
-2.29715650817742 + 1.20562515060291*i

y1=(−12−3i2)1+10593−23(−12−3i2)1+10593y_{1} = \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + \frac{\sqrt{105}}{9}} - \frac{2}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + \frac{\sqrt{105}}{9}}}
=
33(833−(1+3i)2(9+105)23)6(1+3i)9+1053\frac{\sqrt[3]{3} \left(8 \sqrt[3]{3} - \left(1 + \sqrt{3} i\right)^{2} \left(9 + \sqrt{105}\right)^{\frac{2}{3}}\right)}{6 \left(1 + \sqrt{3} i\right) \sqrt[3]{9 + \sqrt{105}}}
=
-0.385458498529624 - 1.56388451052696*i
x2=(−23(−12+3i2)1+10593+(−12+3i2)1+10593)2x_{2} = \left(- \frac{2}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + \frac{\sqrt{105}}{9}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + \frac{\sqrt{105}}{9}}\right)^{2}
=
323(−833+(1−3i)2(9+105)23)236(1−3i)2(9+105)23\frac{3^{\frac{2}{3}} \left(- 8 \sqrt[3]{3} + \left(1 - \sqrt{3} i\right)^{2} \left(9 + \sqrt{105}\right)^{\frac{2}{3}}\right)^{2}}{36 \left(1 - \sqrt{3} i\right)^{2} \left(9 + \sqrt{105}\right)^{\frac{2}{3}}}
=
-2.29715650817742 - 1.20562515060291*i

y2=−23(−12+3i2)1+10593+(−12+3i2)1+10593y_{2} = - \frac{2}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + \frac{\sqrt{105}}{9}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + \frac{\sqrt{105}}{9}}
=
33(833−(1−3i)2(9+105)23)6(1−3i)9+1053\frac{\sqrt[3]{3} \left(8 \sqrt[3]{3} - \left(1 - \sqrt{3} i\right)^{2} \left(9 + \sqrt{105}\right)^{\frac{2}{3}}\right)}{6 \left(1 - \sqrt{3} i\right) \sqrt[3]{9 + \sqrt{105}}}
=
-0.385458498529624 + 1.56388451052696*i
x3=(−231+10593+1+10593)2x_{3} = \left(- \frac{2}{3 \sqrt[3]{1 + \frac{\sqrt{105}}{9}}} + \sqrt[3]{1 + \frac{\sqrt{105}}{9}}\right)^{2}
=
323(−(9+105)23+233)29(9+105)23\frac{3^{\frac{2}{3}} \left(- \left(9 + \sqrt{105}\right)^{\frac{2}{3}} + 2 \sqrt[3]{3}\right)^{2}}{9 \left(9 + \sqrt{105}\right)^{\frac{2}{3}}}
=
0.594313016354849

y3=−231+10593+1+10593y_{3} = - \frac{2}{3 \sqrt[3]{1 + \frac{\sqrt{105}}{9}}} + \sqrt[3]{1 + \frac{\sqrt{105}}{9}}
=
33(−233+(9+105)23)39+1053\frac{\sqrt[3]{3} \left(- 2 \sqrt[3]{3} + \left(9 + \sqrt{105}\right)^{\frac{2}{3}}\right)}{3 \sqrt[3]{9 + \sqrt{105}}}
=
0.770916997059248
Respuesta numérica [src] 
x1 = 0.5943130163548487
y1 = 0.7709169970592481
x1 = 0.5943130163548487
y1 = 0.7709169970592481
    © Sr Examen – Калькулятор