a. If B is a positive number and the equation x square + 2bx + a = 0 and x square + ax + 2B = 0 have a common root on the X axis, what is the minimum value of a square + b square

a. If B is a positive number and the equation x square + 2bx + a = 0 and x square + ax + 2B = 0 have a common root on the X axis, what is the minimum value of a square + b square

Since the parabola has a common point of intersection on the X axis, there exists an X such that: X & sup2; + ax + 2B = x & sup2; + 2bx + a = 0 holds. That is, (a-2b) x = 0, if x = 0, then a = b = 0 does not hold, which is in contradiction with the fact that a and B are positive numbers. Therefore, the a = 2B equation x & sup2; + ax + a = 0 has a solution