Archive
23rd of March 2017
Mathematics
Q:

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

Nisha_vini29 - CBSE - Class IX

Thursday, March 23, 2017 at 17:41:PM

A:

begin mathsize 16px style straight a plus straight b plus straight c space equals 12 comma space straight a squared space plus space straight b squared space plus straight c squared space equals space 90 comma space find space straight a cubed space plus space straight b cubed space plus space straight c cubed space minus 3 abc
Consider comma space 1 over straight a plus 1 over straight b plus 1 over straight c equals space fraction numerator ab plus bc plus ac over denominator abc end fraction
open parentheses straight a plus straight b plus straight c close parentheses squared equals space straight a squared space plus space straight b squared space plus straight c squared space plus 2 left parenthesis ab plus bc plus ac right parenthesis
rightwards double arrow 144 equals 90 space plus 2 left parenthesis ab plus bc plus ac right parenthesis
rightwards double arrow ab plus bc plus ac equals 27
straight a cubed space plus space straight b cubed space plus space straight c cubed space minus 3 abc
equals space left parenthesis straight a space plus space straight b space plus space straight c right parenthesis space left parenthesis space straight a squared space plus space straight b squared space plus straight c squared space space – space ab space – space bc space – space ca right parenthesis space
equals space left parenthesis 12 right parenthesis space left parenthesis space 90 space – space 27 right parenthesis space
equals 756 end style

Thursday, March 23, 2017 at 17:52:PM