NDA Mathematics Question (2025) — Solution

Step-by-step solution

The given equation is x + x = 2 x. Rewriting the equation in terms of x and x: x x + 1 x = 2 x For the equation to be defined, x 0, which means x 2 . Thus, x [0, 2 ). Multiplying both sides by x: x + 1 = 2 ^2 x Substituting ^2 x = 1 - ^2 x: x + 1 = 2(1 - ^2 x) 2 ^2 x + x - 1 = 0 Factoring the quadratic equation: (2 x - 1)( x + 1) = 0 This gives x = 1 2 or x = -1. Since x [0, 2 ), x 0. Therefore, x = -1 is rejected. For x = 1 2 , the only solution in the given interval is x = 6 . Thus, there is exactly 1 value of x satisfying the equation. Answer: 1