Let’s solve the equation step-by-step.
We are given the equation:
[tex]\[ A^2 + B^2 = A^2 + X^2 \][/tex]
To find [tex]\(B\)[/tex], 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]
This simplifies to:
[tex]\[ B^2 = X^2 \][/tex]
2. Take the square root of both sides:
[tex]\[ \sqrt{B^2} = \sqrt{X^2} \][/tex]
Since the square root of [tex]\(B^2\)[/tex] is the absolute value of [tex]\(B\)[/tex], and the square root of [tex]\(X^2\)[/tex] is the absolute value of [tex]\(X\)[/tex], we have:
[tex]\[ |B| = |X| \][/tex]
3. Consider the possible values:
The absolute value equation [tex]\(|B| = |X|\)[/tex] implies that [tex]\(B\)[/tex] can be either [tex]\(X\)[/tex] or [tex]\(-X\)[/tex]:
[tex]\[ B = X \quad \text{or} \quad B = -X \][/tex]
Thus, [tex]\(B\)[/tex] can be [tex]\(\pm X\)[/tex].
Therefore, the correct answer is:
[tex]\[ \text{a) } \pm X \][/tex]
