a) Ta có: \(-x^2+4x-5\)
\(=-\left(x^2-4x+5\right)\)
\(=-\left(x^2-4x+4+1\right)\)
\(=-\left(x-2\right)^2-1\)
Ta có: \(\left(x-2\right)^2\ge0\forall x\)
\(\Leftrightarrow-\left(x-2\right)^2\le0\forall x\)
\(\Leftrightarrow-\left(x-2\right)^2-1\le-1< 0\forall x\)
hay \(-x^2+4x-5< 0\forall x\)(đpcm)
b) Ta có: \(x^4\ge0\forall x\)
\(3x^2\ge0\forall x\)
Do đó: \(x^4+3x^2\ge0\forall x\)
\(\Leftrightarrow x^4+3x^2+3\ge3>0\forall x\)
hay \(x^4+3x^2+3>0\forall x\)(đpcm)
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