\(\Leftrightarrow x^2-5x+7-\frac{1}{2}>0\Leftrightarrow\left(x^2-\frac{2.5}{2}x+\frac{25}{4}\right)+\left(7-\frac{1}{2}-\frac{25}{4}\right)>0\)
\(\Leftrightarrow\left(x-\frac{5}{2}\right)^2+\left(\frac{7.4-2-25}{4}\right)>0\)
<=> (x-5/2)^2+1/4>0
(x-5/2)^2>=0=> (x-5/2)^2+1/4>=1/4>0 => dpcm
\(\)
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A = X2-5X+7>1/2
= 2X2-10X+14>1
=(X2+4X+4)+(X2+6X+9)+1
= (X+2)2+(X+3)2+1
Vi (X+2)2>0 va (X+3)2>0 Nen (X+2)2+(X+3)2+1> 1
Vay 2X2-10X+14>1(dpcm)
=> X2-5X+7>1/2
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