To solve the equation [tex]\(A^2 + B^2 = A^2 + X^2\)[/tex], we can follow these steps:
1. Subtract [tex]\(A^2\)[/tex] from both sides:
[tex]\[
A^2 + B^2 - A^2 = A^2 + X^2 - A^2
\][/tex]
Simplifying this, we get:
[tex]\[
B^2 = X^2
\][/tex]
2. Take the square root of both sides:
[tex]\[
\sqrt{B^2} = \sqrt{X^2}
\][/tex]
Remembering that the square root of a square yields both a positive and a negative solution, we obtain:
[tex]\[
B = \pm X
\][/tex]
Thus, the value of [tex]\(B\)[/tex] that satisfies the equation [tex]\(A^2 + B^2 = A^2 + X^2\)[/tex] is [tex]\(B = \pm X\)[/tex].
Therefore, the correct answer is:
a) [tex]\(\pm X\)[/tex]
