17. If a + b + c = 4 and a ^ 2 + b ^ 2 + c ^ 2 = 55/2 then find the value of a ^ 3 + b ^ 3 + c ^ 3 - 3abc

Asked by dalalvansh4 | 2nd Jun, 2022, 07:03: PM

Expert Answer:

open parentheses straight a plus straight b plus straight c close parentheses squared equals straight a squared plus straight b squared plus straight c squared plus 2 open parentheses ab plus bc plus ca close parentheses
4 squared equals 55 over 2 plus 2 open parentheses ab plus bc plus ca close parentheses
rightwards double arrow 2 left parenthesis ab plus bc plus ca right parenthesis equals 16 minus 55 over 2 equals fraction numerator 32 minus 55 over denominator 2 end fraction equals negative 23 over 2
rightwards double arrow ab plus bc plus ca equals negative 23 over 4

open parentheses straight a cubed plus straight b cubed plus straight c cubed close parentheses minus 3 abc equals open parentheses straight a squared plus straight b squared plus straight c squared minus ab minus bc minus ca close parentheses open parentheses straight a plus straight b plus straight c close parentheses
equals open parentheses 55 over 2 plus 23 over 4 close parentheses open parentheses 4 close parentheses
equals open parentheses fraction numerator 110 plus 23 over denominator 4 end fraction close parentheses 4
equals 133

Answered by Renu Varma | 6th Jun, 2022, 11:00: AM