OG详解-OG3 数学1 Q20

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.