JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

The given equation is |x^2 + x - 9| = |x| + |x^2 - 9|. Let A = x and B = x^2 - 9. Then A + B = x^2 + x - 9. The equation is of the form |A + B| = |A| + |B|, which holds true if and only if A B 0. Substituting the values of A and B: x(x^2 - 9) 0 x(x - 3)(x + 3) 0 The critical points are -3, 0, 3. Using the wavy curve method, the solution set is: x [-3, 0] [3, ) Comparing this with the given solution set [ , ] [ , ), we get: = -3, = 0, = 3 We need to find the value of ^2 + ^2 + ^2: ^2 + ^2 + ^2 = (-3)^2 + 0^2 + 3^2 = 9 + 0 + 9 = 18 Answer: 18