Explanation

x² = (2+√2)² = 6+4√2 and x⁴ = (6+4√2)² = 68+48√2. Also x⁻⁴ = 1/(68+48√2) = (68−48√2)/16, so 16x⁻⁴ = 68−48√2. Adding gives 136. The keyed option is C.