If (x + y)3 + 27 (x - y)3 = (Ax - 2y) (Bx2 + Cxy + 13 y2), then the value of A - B - C is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 13.
we know that, x3 + y3 = (x + y)(x2 - xy + y2)
⇒ (x + y)3 + 27 (x - y)3 = (Ax - 2y) (Bx2 + Cxy + 13 y2)
⇒ (x + y)3 + (3x - 3y)3 = (Ax - 2y) (Bx2 + Cxy + 13 y2)
⇒ (x + y + 3x - 3y) [(x + y)2 + (3x - 3y)2 - (x + y)(3x - 3y)] = (Ax - 2y) (Bx2 + Cxy + 13 y2)
⇒ (4x - 2y)[x2 + y2 + 2xy + 9x2 + 9y2 - 18xy - 3x2 + 3y2] = (Ax - 2y) (Bx2 + Cxy + 13 y2)
⇒ (4x - 2y)[7x2 - 16xy + 13y2] = ( Ax - 2y) (Bx2 + Cxy + 13 y2)
On comparing LHS and RHS one gets,
A = 4 , B = 7 और C = -16
Now A - B - C = 4 - 7 +16 = 13