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

Asked by Vikas | 4th Jul, 2017, 10:07: AM

Expert Answer:

begin mathsize 16px style straight a plus straight b plus space straight c space equals space 12
straight a squared space plus straight b squared space plus straight c squared space equals 90

left parenthesis straight a plus straight b plus straight c right parenthesis squared equals straight a squared plus straight b squared plus straight c squared plus 2 left parenthesis ab plus bc plus ca right parenthesis
rightwards double arrow left parenthesis 12 right parenthesis squared equals 90 plus 2 left parenthesis ab plus bc plus ca right parenthesis
rightwards double arrow 144 equals 90 plus 2 left parenthesis ab plus bc plus ca right parenthesis
rightwards double arrow 2 left parenthesis ab plus bc plus ca right parenthesis equals 54
rightwards double arrow ab plus bc plus ca equals 27

Now comma space straight a cubed space plus straight b cubed space plus straight c cubed space minus 3 abc
equals left parenthesis straight a plus straight b plus straight c right parenthesis left square bracket left parenthesis straight a squared plus straight b squared plus straight c squared right parenthesis minus left parenthesis ab plus bc plus ca right parenthesis right square bracket
equals 12 cross times open square brackets 90 minus 27 close square brackets
equals 12 cross times 63
equals 756 end style

Answered by Rashmi Khot | 4th Jul, 2017, 11:35: AM