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miko_tinhnghich_dangyeu

phuong287 said:
Cmr: Với a,b>0 thì
[TEX]\frac{a}{b}+\frac{b}{a}+4\sqrt[]{2}\frac{a+b}{\sqrt[]{a^2+b^2}} \geq 10[/TEX]
Bấm để xem đầy đủ nội dung ...
ta cần cm :
[TEX]\frac{a+b}{\sqrt{a^2+b^2}}\geq\sqrt{2} (1)[/TEX]
[TEX]\Rightarrow \frac{(a+b)^2}{a^2+b^2}\geq2 (a,b>0)[/TEX]
[TEX]\Leftrightarrow 2(a^2+b^2)\geq (a+b)^2[/TEX]
[TEX]\Rightarrow[/TEX] luôn đúng ->(1)đúng
[TEX]\frac{a}{b}+\frac{b}{a}\geq2[/TEX]
[TEX]\Rightarrow[/TEX] đpcm
 
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