Question

tìm GTNN 2x^2 -x-1

Answer 1

\(=2\left(x^2-\dfrac{1}{2}x-\dfrac{1}{2}\right)\\ =2\left(x^2-2.\dfrac{1}{4}x+\dfrac{1}{16}-\dfrac{9}{16}\right)\\ =2\left(x-\dfrac{1}{4}\right)^2-\dfrac{9}{16}\ge-\dfrac{9}{16}\forall x\\ \)

Dấu bằng xảy ra khi

\(x-\dfrac{1}{4}=0\\ x=\dfrac{1}{4}\)

Vậy GTNN = \(-\dfrac{9}{16}khix=\dfrac{1}{4}\)

Answer 2

\(=2\left(x^2-\dfrac{1}{2}x-\dfrac{1}{2}\right)\)

\(=2\left(x^2-2\cdot x\cdot\dfrac{1}{4}+\dfrac{1}{16}-\dfrac{9}{16}\right)\)

\(=2\left(x-\dfrac{1}{4}\right)^2-\dfrac{9}{8}>=-\dfrac{9}{8}\)

Dấu '=' xảy ra khi x=1/4

Answer 3

= 2x^2 +x -2x -1
=x(2x+1)-(2x+1)
=(2x+1)(x-1)