Question

If a*2+b*2+c*2=250 and ab +bc+ca=3. then find value of a*3+b*3+c*3

Answer 1

Given :  a² +b² + c²  = 250   , ab  + bc + ca = 3

To find : Value of a + b + c  ( correction in Question)

Solution:

a² +b² + c²  = 250

ab  + bc + ca = 3

(a + b + c)² = a² +b² + c² + 2(ab + bc + ca)

=> (a + b + c)² =  250 + 2(3)

=> (a + b + c)² =  256

=> a + b + c  =   ±16

value of a + b + c  =   ±16

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

=>  a³+b³+c³ - 3abc  = ±16 (250 - 3)

=> a³+b³+c³ - 3abc  = ±3952

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