a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/06 12:39:16
![a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9](/uploads/image/z/572409-9-9.jpg?t=a%3E0+b%3E0+c%3E0+a%2Bb%3D1+%E8%AF%81%281-1%2Fa%5E2%29%281-1%2Fb%5E2%29%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E9a%3E0+b%3E0+c%3E0+a%2Bb%3D1+%E8%AF%81%281-1%2Fa%5E2%29%281-1%2Fb%5E2%29%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E9)
x)K3PHd NN5TxQPP?1HH2.YdW@Ғ=6IEdYFF;:{S
X6PWhfH6TQa
RL*0I FqZIFI@*QS_*T.Kŵ4m7z6}۳ WwC5 1z
ǵ
a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9
a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9
a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9
a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9a>0 b>0 c>0 a+b=1 证(1-1/a^2)(1-1/b^2)大于等于9
(1-1/a^2)(1-1/b^2)
=[1-(a+b)^2/a^2][1-(a+b)^2/b^2]
=(2ab+b^2)/a^2*(2ab+a^2)/b^2
=(5a^2*b^2+2a^3*b+2b^3*a)/(a^2*b^2)
=5+2(a^2*b^2)/(ab)
>=5+2*2ab/(ab) (a=b=1/2时成立)
=9