Maths Olympiad Prep

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Algebra Difficulty 5.9 AIME, harder Find the answer

28. Given the following 3 propositions: (1) If a,bRa, b \in \mathrm{R}, then a+b2\frac{a+b}{2} ab\geqslant \sqrt{a b}; (2) xRx \in \mathrm{R}, then x2+1>xx^{2}+1>x; (3) If xRx \in \mathrm{R} and x0x \neq 0, then x+1x2x+\frac{1}{x} \geqslant 2, the true propositions are \qquad.

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Solution

28. (2);

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