Explanation

Work from the outside in. Raising both sides to the power −2 gives [1 − {1 − (1−x²)⁻¹}⁻¹]⁻¹ = 100, i.e. the bracket equals 1/100. Hence {1 − (1−x²)⁻¹}⁻¹ = 99/100, so 1 − (1−x²)⁻¹ = 100/99 and (1−x²)⁻¹ = −1/99. Inverting, 1−x² = −99, so x² = 100. Taking the positive listed value, x = 10 (option B); the negative root −10 is not among the options.