Question

If \( \frac{1}{x^2 - 2} = \frac{1}{7} \), then the value of \( x \) will be:

• A. \(\pm 2\)
• B. \(\pm 1\)
• C. \(\pm 3\)
• D. \(\pm 5\)

Hint:

When solving equations involving squares, remember to consider both the positive and negative roots, as both are valid solutions when squaring.

Answer 1

The Correct Option is C

We are given the equation: \[ \frac{1}{x^2 - 2} = \frac{1}{7} \]
Step 1: Cross multiply to eliminate the fractions.
To simplify the equation, we cross-multiply both sides: \[ 1 \times 7 = (x^2 - 2) \times 1 \] This simplifies to: \[ 7 = x^2 - 2 \]
Step 2: Isolate \( x^2 \).
Now, add 2 to both sides to isolate \( x^2 \): \[ 7 + 2 = x^2 \] \[ x^2 = 9 \]
Step 3: Solve for \( x \).
Taking the square root of both sides: \[ x = \pm \sqrt{9} \] \[ x = \pm 3 \]
Step 4: Conclusion.
Thus, the value of \( x \) is \( \pm 3 \). The correct answer is (C).