趣味的数学-115
a和b是正实数，且以下两个二次方程
x^2 + ax + 2b = 0 和
x^2 + 2bx + a = 0
都有实数根。求a+b的最小值。
【AHSMC】
是
6
(x+1/2a)^2 = 1/4a^2 - 2b (1)
(x + b) ^2 = b^2 - a (2)
from 1-2:
a^2 >=8b (3)
b^2 >= a (4)
since a>=0, and b >= 0,
from 3-4:
a^2 >= 8 a^1/2 =>
a>= 4
and back into 4, we have:
b>=2
a +b >= 6
