anh19101997

Bài 375:
Ta chứng minh bđt sau
$\large \dpi{100} (1-a^{2})(1-b^{2})\geq (1-ab)^{2}$ (dễ chứng minh)
Ta có:$\large \dpi{100} ab+bc+ca= 1$ nên $\large \dpi{100} (1-ab)^{2}=(ac+bc)^{2}=c^{2}(a+b)^{2}$
Suy ra$\large \dpi{100} (1-a^{2})(1-b^{2})\leq (c^{2})(a+b)^{2}$
Cm tương tự$\large \dpi{100} (1-b^{2})(1-c^{2})\leq (a^{2})(b+c)^{2}$
$\large \dpi{100} (1-c^{2})(1-a^{2})\leq (b^{2})(a+c)^{2}$
Suy ra đpcm

BÀi 375: $a,b,c> 0, ab+bc+ca=1$ cmr
$$(1-a^{2})(1-b^{2})(1-c^{2})\leq abc(a+b)(b+c)(c+a)$$