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[eminemdech]

Chứng minh $2a^4+\frac{1}{1+a^2}\geq 3a^2-1$

[vutienhoang]

bđt <=>$(a^2-1)(2a^2-1)+\frac{1}{a^2+1}\geq 0$
nếu $a^2\geq$1 hoăc $a^2\leq 1/2$ thì bđt luôn đúng
nếu $1\geq a^2\geq \frac{1}{2}$ có $(a^2-1)(2a^2-1)=-(1-a^2)(2a^2-1)\geq -(\frac{a^2}{2})^2\geq -\frac{1}{4}$ có $\frac{1}{a^2+1}\geq \frac{1}{2}$ => bđt đúng