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T

tuyetnhung198

[tex]x^2+y^2=1 \\ CMR: \ x\sqrt{y+1}+y\sqrt{x+1} \leq \ \sqrt{2+\sqr{2}}[/tex]

Use Bunyacopsky's :):):)************************************************************************************************....................
 
L

letuananh1991

áp dụng bunhia........

[TEX] (x\sqrt[]{y+1} + y\sqrt[]{x+1})^2 \leq (x^2+y^2)(x+y+2)[/TEX]

[TEX]\leq \sqrt[]{(1+1)(x^2+y^2)+2} = \sqrt[]{2+\sqrt[]{2}}[/TEX]

dấu [TEX]"="[/TEX] khi [TEX]x=y=+-\frac{1}{\sqrt[]{2}}[/TEX]
 
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