MathDB
9^{x+1} + 2187 = 3^{6x-x^2}

Source: 2023 NZMO - New Zealand Maths Olympiad Round 1 p3

September 2, 2023
algebra

Problem Statement

Find the sum of the smallest and largest possible values for xx which satisfy the following equation. 9x+1+2187=36xāˆ’x2.9^{x+1} + 2187 = 3^{6x-x^2}.