如何证明√x1x2≤(x1+x2)/2≤√(x1^2+x2^2)/2_数学解答

如何证明√x1x2≤(x1+x2)/2≤√(x1^2+x2^2)/2

人气：363 ℃　时间：2020-07-13 14:45:22

解答

(x1^2+x2^2)/2-[(x1+x2)/2]^2
=(x1^2-2x1x2+x2^2)/4
=(x1-x2)^2/4>=0,
[(x1+x2)/2]^2-x1x2
=(x1^2-2x1x2+x2^2)/4
=(x1-x2)^2/4>=0,
∴x1x2