a. \(x^2+3x+5\)
\(=x^2+2.x^2.\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{11}{4}\)
\(=\left(x+\dfrac{3}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\)
=> đpcm
b. \(4x^2+5x+7\)
\(=\left(2x\right)^2-2.2x.\dfrac{5}{4}+\dfrac{25}{16}+\dfrac{87}{16}\)
= \(\left(2x+\dfrac{5}{4}\right)^2\) + \(\dfrac{87}{16}\) \(\ge\dfrac{87}{16}\)
=> đpcm
c. \(6x-9x^2-4\)
=> \(-9x^2+6x-4\)
\(=-\left(9x^2-6x+4\right)\)
\(=-[\left(3x\right)^2-2.3x.1+1-5]\)
\(=\left(3x-1\right)^2\le5\forall x\)
=> đpcm
e. \(2x-3x^2-5\)
\(=-3x^2+2x-5\)
\(=-3\left(x^2-\dfrac{2}{3}+\dfrac{5}{3}\right)\)
\(=-3\left(x^2-2.x.\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{14}{9}\right)\)
\(=-3\left(x-\dfrac{1}{3}\right)^2+\dfrac{14}{3}\ge0\forall x\)
=> đpcm
Bạn ơi bạn xem lại đề này nhé
