x^2+y^2=60 and x-y=6,then find the value of x^3-y^3

Asked by dollyjacob1976 | 12th Aug, 2016, 01:31: PM

Expert Answer:

begin mathsize 16px style straight x squared plus straight y squared equals 60 space and space straight x minus straight y equals 6
rightwards double arrow straight x squared plus straight y squared minus 2 xy equals 60 minus 2 xy
rightwards double arrow left parenthesis straight x minus straight y right parenthesis squared equals 60 minus 2 xy
rightwards double arrow left parenthesis 6 right parenthesis squared equals 60 minus 2 xy
rightwards double arrow 36 equals 60 minus 2 xy
rightwards double arrow negative 24 equals negative 2 xy
rightwards double arrow xy equals 12.... space left parenthesis straight i right parenthesis
straight x cubed minus straight y cubed equals left parenthesis straight x minus straight y right parenthesis left parenthesis straight x squared plus straight y squared plus xy right parenthesis
space space space space space space space space space space space equals left parenthesis 6 right parenthesis left parenthesis 60 plus 12 right parenthesis... left parenthesis from space left parenthesis straight i right parenthesis right parenthesis
space space space space space space space space space space space equals 432
So comma space straight x cubed minus straight y cubed equals 432 end style

Answered by Rebecca Fernandes | 12th Aug, 2016, 03:58: PM