Question

已知抛物线Y=X^2-2(m+1)x+m^2 与x轴的两个交点的 （第11题） 横坐标均为整数,且m

Answer 1

y = x^2 -2(m+1)x + m^2 = 0

∆ = 4(m+1)^2 - 4m^2 = 4(2m+1)

x = [2(m+1) ± √4(2m+1)]/2 = (m+1) ± √(2m+1)

与x轴的两个交点的横坐标均为整数,则2m+1为平方数:

m = 0时,2m+1 =1

m = 4时,2m+1 = 9

即m = 0 或 m = 4