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\\frac{\\alpha_{2}}{A(a,b)}+\\frac{1-\\alpha_{2}}{\\bar{C}(a,b)}<\\frac1{T(a,b)} <\\frac{\\beta_{2}}{A(a,b)}+\\frac{1-\\beta_{2}}{\\bar{C}(a,b)} $$ to be valid for all $a,b>0$ with $a\\ne b$, where $$ \\bar{C}(a,b)=\\frac{2(a^{2}+ab+b^{2})}{3(a+b)},\\quad A(a,b)=\\frac{a+b}2, $$ and $$ 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