Tácticas matemáticas.

[j2e2xae]

a + b + c  =  0

a³ + b³ + c³  =  a⁵ + b⁵ + c⁵


demostrar


a² + b² + c²  =  6 / 5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

   Resolveremos el problema utilizando funciones simétricas ...

e₁ = p₁ = 0

p₃ = p₅

e_n = 0 , n > 3

 

donde e_n representan a las funciones simétricas elementales y p_n a las funciones simétricas de las sumas de potencias.

Expresando las sumas de potencias en función de las funciones unitarias.

p₂ = −2 e₂       

p₃ =   3 e₃       

p₅ = −5 e₂ e₃


p₃ = p₅

3 e₃ = −5 e₂ e₃

e₂ = − 3 / 5


∴   p₂ = 6 / 5

 

∎

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