The Expression Undetermined error: @@(X+Y)^n -Y^n -X^n@@ (Where 'n' is an odd number,but not a multiple of 3)is divisible by:
(a)Undetermined error: @@(X+Y)(X+XY+Y)@@
(b)Undetermined error: @@(X+Y)(X^2 +XY +Y^2)@@
(c)Undetermined error: @@(X+Y)(X+2XY+Y)@@
(d)Undetermined error: @@(X+XY+Y)(X-XY+Y) @@
I got the answer as (b).
Another factor i got was XY.
Another factor i got was XY.
Ankul you got it absolutely right !! But would be kind enough to tell me the method to solve it.Please reply.
See for i) x = 0, ii) y=0, iii) x= -y
the expression reduces to 0
Hence, xy(x+y) is a factor.
Also, for i) x=y*omega, ii) x = y*(omega)2
the expression again reduces to 0.
Therefore, x2+xy+y2 is also a factor. I hope u should be able to make that.
Note: (x-y*omega)(x-y*(omega)2) = x2+ xy + y2
Thus collectively, the expression is divisible by xy(x+y)(x2+xy+y2)
the expression reduces to 0
Hence, xy(x+y) is a factor.
Also, for i) x=y*omega, ii) x = y*(omega)2
the expression again reduces to 0.
Therefore, x2+xy+y2 is also a factor. I hope u should be able to make that.
Note: (x-y*omega)(x-y*(omega)2) = x2+ xy + y2
Thus collectively, the expression is divisible by xy(x+y)(x2+xy+y2)
Great method applied !!.Thanks, Ankul for kindly sending me the detailed solution.