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sqrt(x)+sqrt(y)=10; sqrt(x)^4+sqrt(y)^4=4

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Solución

Ha introducido [src]
  ___     ___     
\/ x  + \/ y  = 10
x+y=10\sqrt{x} + \sqrt{y} = 10
     4        4    
  ___      ___     
\/ x   + \/ y   = 4
(x)4+(y)4=4\left(\sqrt{x}\right)^{4} + \left(\sqrt{y}\right)^{4} = 4
(sqrt(x))^4 + (sqrt(y))^4 = 4
Respuesta rápida
x1=21000i755002+205002i755002x_{1} = \sqrt{2 - 1000 i \sqrt{75 - \sqrt{5002}} + 20 \sqrt{5002} i \sqrt{75 - \sqrt{5002}}}
=
21000i755002+205002i755002\sqrt{2 - 1000 i \sqrt{75 - \sqrt{5002}} + 20 \sqrt{5002} i \sqrt{75 - \sqrt{5002}}}
=
20.7248188403477 + 20.6765112135783*i

y1=50+500210i755002y_{1} = -50 + \sqrt{5002} - 10 i \sqrt{75 - \sqrt{5002}}
=
50+500210i755002-50 + \sqrt{5002} - 10 i \sqrt{75 - \sqrt{5002}}
=
20.7248188403477 - 20.6765112135783*i
x2=2+1000i5002+75+205002i5002+75x_{2} = - \sqrt{2 + 1000 i \sqrt{\sqrt{5002} + 75} + 20 \sqrt{5002} i \sqrt{\sqrt{5002} + 75}}
=
2+1000i5002+75+205002i5002+75- \sqrt{2 + 1000 i \sqrt{\sqrt{5002} + 75} + 20 \sqrt{5002} i \sqrt{\sqrt{5002} + 75}}
=
-120.724818840348 - 120.716535255261*i

y2=500250+10i5002+75y_{2} = - \sqrt{5002} - 50 + 10 i \sqrt{\sqrt{5002} + 75}
=
500250+10i5002+75- \sqrt{5002} - 50 + 10 i \sqrt{\sqrt{5002} + 75}
=
-120.724818840348 + 120.716535255261*i
x3=2205002i755002+1000i755002x_{3} = \sqrt{2 - 20 \sqrt{5002} i \sqrt{75 - \sqrt{5002}} + 1000 i \sqrt{75 - \sqrt{5002}}}
=
2205002i755002+1000i755002\sqrt{2 - 20 \sqrt{5002} i \sqrt{75 - \sqrt{5002}} + 1000 i \sqrt{75 - \sqrt{5002}}}
=
20.7248188403477 - 20.6765112135783*i

y3=50+5002+1075+5002y_{3} = -50 + \sqrt{5002} + 10 \sqrt{-75 + \sqrt{5002}}
=
50+5002+1075+5002-50 + \sqrt{5002} + 10 \sqrt{-75 + \sqrt{5002}}
=
20.7248188403477 + 20.6765112135783*i
x4=2205002i5002+751000i5002+75x_{4} = - \sqrt{2 - 20 \sqrt{5002} i \sqrt{\sqrt{5002} + 75} - 1000 i \sqrt{\sqrt{5002} + 75}}
=
2205002i5002+751000i5002+75- \sqrt{2 - 20 \sqrt{5002} i \sqrt{\sqrt{5002} + 75} - 1000 i \sqrt{\sqrt{5002} + 75}}
=
-120.724818840348 + 120.716535255261*i

y4=50025010i5002+75y_{4} = - \sqrt{5002} - 50 - 10 i \sqrt{\sqrt{5002} + 75}
=
50025010i5002+75- \sqrt{5002} - 50 - 10 i \sqrt{\sqrt{5002} + 75}
=
-120.724818840348 - 120.716535255261*i
Respuesta numérica [src]
x1 = 20.7248188403485 + 20.67651121357786*i
y1 = 20.72481884034669 - 20.67651121357728*i
x2 = 20.72481884034769 + 20.67651121357834*i
y2 = 20.72481884034769 - 20.67651121357834*i
x3 = 20.72481884034844 + 20.67651121357805*i
y3 = 20.72481884034765 - 20.67651121357853*i
x4 = -120.7248188403477 - 120.7165352552614*i
y4 = -120.7248188403477 + 120.7165352552614*i
x4 = -120.7248188403477 - 120.7165352552614*i
y4 = -120.7248188403477 + 120.7165352552614*i