AP EAMCET201921 Apr 2019Evening ShiftMathematicsBasics of MathematicsActual
Which of the following is divisible by x 2 - y 2 , ∀ x ≠ y ?
Options
- Ax n - y n   ∀   n ∈ N
- Bx n + y n   ∀   n ∈ N
- Cx n - y n x 2 n + 1 + y 2 n + 1   ∀   n ∈ N
- Dx n - y n x m + y m   ∀   m ,   n ∈ N
Correct answer
C. x n - y n x 2 n + 1 + y 2 n + 1   ∀   n ∈ N
Step-by-step solution
The expression x n - y n is divisible by ( x + y ) ( x - y ) , if n = even. Similarly, x n - y n is divisible by ( x - y ) , if n = odd and x 2 n + 1 + y 2 n + 1 is divisible by ( x + y ) .