Nếu \(x^2-9x+14=\left(x-7\right)\left(x-2\right)\ge0\)
\(\Leftrightarrow\)\(x\ge7;\)\(x\le2\)
thì \(\left|x^2-9x+14\right|=x^2-9x+14\)
Khi đó bpt trở thành: \(x^2-9x+14+3x>x^2-4\)
\(\Leftrightarrow\)\(-6x>-18\)
\(\Leftrightarrow\) \(x< 3\)(thỏa mãn)
Nếu \(x^2-9x+14=\left(x-7\right)\left(x-2\right)< 0\)
\(\Leftrightarrow\)\(2< x< 7\)
thì \(\left|x^2-9x+14\right|=-x^2+9x-14\)
Khi đó bpt trở thành: \(-x^2+9x-14+3x>x^2-4\)
\(\Leftrightarrow\)\(-2x^2+12x-10>0\)
\(\Leftrightarrow\) \(x^2-6x+5< 0\)
\(\Leftrightarrow\)\(\left(x-1\right)\left(x-5\right)< 0\)
\(\Leftrightarrow\) \(1< x< 5\) (thỏa mãn)
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