OG详解-OG9 数学1 Q21

The correct answer is -3. Squaring both sides of the given equation yields (x-2)² = 3x+34, which can be rewritten as x² -4x+4 = 3x+34. Subtracting 3x and 34 from both sides of this equation yields x² -7x-30 = 0. This quadratic equation can be rewritten as (x-10)(x+3) = 0. According to the zero product property, (x-10)(x+3) equals zero when either x- 10 = 0 or x+3 = 0. Solving each of these equations for x yields x = 10 or x =-3. Therefore, the given equation has two solutions, 10 and -3. Of these two solutions, -3 is the smallest solution to the given equation.