Question

If a+b+c = 5 and ab + bc + c = 10 , prove that a³ + b³ + c³ - 3abc = -25

Answer 1

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Answer 2

a+b+c = 5 and ab + bc + c = 10 , prove that a³ + b³ + c³ - 3abc = -25

(a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca
     (5)²     = a² + b² + c² + 2(10)
     25      =  a² + b² + c²  + 20
 25 - 20  = a² + b² + c² 
      5       = a² + b² + c² 

a³ + b³ + c³ - 3abc  = (a+b+c) [a² + b² + c² - (ab+bc+ca)]
a³ + b³ + c³ - 3abc  = (5) (5 - 10)
a³ + b³ + c³ - 3abc  = 5 x (-5)
a³ + b³ + c³ - 3abc  = -25

Hence proved!