Question

Find Q in the following equation:

Q±Q = (A^n)±A
A) n(A^(n-1))±A
B) n(A^(n+1))±A
C) n(A^n)^(n-1)±A
D) n(A^n)^(n+1)±A

Answer 1

A) n(A^(n-1))±A

The provided equation Q ± Q = (A^n) ± A simplifies to 0 = A^n ± A, and none of the answer choices correctly represent the simplified equation as the left side is zero, indicating a potential error in the question itself.

Step-by-step explanation:

To find Q in the given equation Q ± Q = (A^n) ± A, we need to simplify using algebra. Let us apply the distributive property to the equation, assuming an implicit multiplication by 1 for Q:

Q(1 ± 1) = A(A^{n-1} ± 1)

Since 1 ± 1 is zero, the left side of the equation becomes 0. For the right side of the equation, we need to distribute A across the terms within the parenthesis, which results in:

A(A^{n-1}) ± A = A^n ± A

Therefore, we deduce that none of the provided answer choices A) n(A^(n-1))±A B) n(A^(n+1))±A C) n(A^n)^(n-1)±A D) n(A^n)^(n+1)±A correctly simplifies the given equation because the left side zeroes out and does not match with any of the proposed choices. Thus, the question seems to contain an error.