chung minh bat dang thuc sau

T

thienvamai

[TEX]\sqrt{a^2+b^2}+\sqrt{b^2+c^2}+\sqrt{c^2+a^2}\geq \sqrt{2}[/TEX]
[TEX]\Leftrightarrow 2a^2+2b^2+2c^2+2\sqrt{(a^2+b^2)(b^2+c^2)}+2\sqrt{(c^2+b^2)(c^2+a^2)}+2\sqrt{(a^2+b^2)(a^2+c^2)} \geq2 [/TEX]
Có[TEX]2\sqrt{(a^2+b^2)(b^2+c^2)} \geq 2\sqrt{(ab+bc)^2}=2ab+2bc [/TEX]
[TEX]\Rightarrow2a^2+2b^2+2c^2+2\sqrt{(a^2+b^2)(b^2+c^2)}+2\sqrt{(c^2+b^2)(c^2+a^2)}+2\sqrt{(a^2+b^2)(b^2+c^2)} \geq 2(a^2+b^2+c^2+2ab+2ac+2bc)=2(a+b+c)^2=2[/TEX]
\Rightarrowđpcm
 
You must log in or register to reply here.
Top Bottom