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If $s_{1}\ge t_{1}\ge t_{2}\ge s_{2}\ge0$, does one always have $(s_{1}-t_{1}+s_{2}+t_{2})^{1/2}\ge\sqrt{s_{1}}-\sqrt{t_{1}}+\sqrt{t_{2}}-\sqrt{s_{2}}$? Thanks a lot!

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    Welcome to math.stackexchange! Did you try to take the squares?2012-01-21
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    Yes, I tried to take the squares. After cancellations, it becomes $\sqrt{s_{1}t_{1}}+\sqrt{t_{1}t_{2}}+\sqrt{s_{2}t_{2}}+\sqrt{s_{1}s_{2}}\ge\sqrt{s_{1}t_{2}}+\sqrt{s_{2}t_{1}}+t_{1}$. Is this true for all $s_{1}\ge t_{1}\ge t_{2}\ge s_{2}\ge0$?2012-01-21
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    I got the same; the main difficulty lies in comparing $\sqrt{s_1t_2}$ with $\sqrt{s_1s_2}+\sqrt{s_2t_2}$; perhaps find conditions for the former to be larger than the latter?2012-01-21
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    Please choose more specific and descriptive titles for your questions. The purpose of the title is to summarize the question so as to represent it e.g. in the list of questions on the main page. To see why this title wasn't a good choice, imagine how that page would look if all users were to choose titles like this.2012-01-22

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