Explanation

Apply componendo–dividendo to x = (√(a+2b)+√(a−2b))/(√(a+2b)−√(a−2b)): (x+1)/(x−1) = √(a+2b)/√(a−2b). Squaring and cross-multiplying gives (a−2b)(x+1)² = (a+2b)(x−1)². Expanding and simplifying yields 4ax−4b(x²+1) = 0, i.e. bx²−ax+b = 0, so the expression equals 0, option A.