If a + b + c = 12 , a2 + b2 + c2 = 90, find the value of a3 + b3 + c3 - 3 abc ?

Asked by nisha_vini29 | 1st Jul, 2017, 09:38: AM

Expert Answer:

begin mathsize 16px style straight a plus straight b plus straight c equals 12
rightwards double arrow open parentheses straight a plus straight b plus straight c close parentheses squared equals 12 squared
rightwards double arrow straight a squared plus straight b squared plus straight c squared plus 2 left parenthesis ab plus bc plus ac right parenthesis equals 144
rightwards double arrow 90 plus 2 left parenthesis ab plus bc plus ac right parenthesis equals 144
rightwards double arrow ab plus bc plus ac equals 27
straight a cubed plus straight b cubed plus straight c cubed minus 3 abc equals left parenthesis straight a plus straight b plus straight c right parenthesis left parenthesis straight a squared plus straight b squared plus straight c squared minus ab minus bc minus ac right parenthesis
rightwards double arrow straight a cubed plus straight b cubed plus straight c cubed minus 3 abc equals left parenthesis 12 right parenthesis left parenthesis 90 minus 27 right parenthesis
rightwards double arrow straight a cubed plus straight b cubed plus straight c cubed minus 3 abc equals left parenthesis 12 right parenthesis left parenthesis 63 right parenthesis
rightwards double arrow straight a cubed plus straight b cubed plus straight c cubed minus 3 abc equals 756 end style

Answered by Rebecca | 1st Jul, 2017, 11:14: PM