6. \(-2x^2+2x-4=-2\left(x^2-x+2\right)\)
\(=-2\left(x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}+2\right)\)
\(=-2\left[\left(x-\dfrac{1}{2}\right)^2+\dfrac{7}{4}\right]\)
\(=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{7}{2}\le\dfrac{-7}{2}< 0\)
-> ĐPCM.
7. 8. 9 Tương tự
10. \(6x^2+15x-21\)
\(=6\left(x^2+\dfrac{15}{6}x-\dfrac{7}{2}\right)\)
\(=6\left(x^2+2.x.\dfrac{5}{4}+\dfrac{25}{16}-\dfrac{25}{16}-\dfrac{7}{2}\right)\)
\(=6\left[\left(x+\dfrac{5}{4}\right)^2-\dfrac{81}{16}\right]\)
\(=6\left(x+\dfrac{5}{4}\right)^2-\dfrac{243}{8}\)
\(=\dfrac{243}{8}-6\left(x+\dfrac{5}{4}\right)^2\)
....
1)
-2x2+2x-4
= -2(x2 -x +2)
= -2(x2 - 2.\(\dfrac{1}{2}\).x + \(\dfrac{1}{4}\)+\(\dfrac{7}{4}\))
= -2.(x-\(\dfrac{1}{2}\))2 - \(\dfrac{7}{2}\) \(\le\) - \(\dfrac{7}{2}\) với \(\forall\) x
=> -2x2+2x-4 luôn âm
=>đpcm
2)
-2x2 +6x -8
= -2 (x2 -3x + 4)
= -2(x2 - 2.\(\dfrac{3}{2}\).x +\(\dfrac{9}{4}\)+\(\dfrac{7}{4}\))
= -2.(x-\(\dfrac{3}{2}\))2 - \(\dfrac{7}{2}\) \(\le\) - \(\dfrac{7}{2}\) với \(\forall\) x
=> -2x2 +6x -8 luôn âm
=>đpcm
3)
-x2 + 4x -1
= - (x2 - 4x +1)
= -(x2 - 2.2.x + 4 -3)
= -(x - 2)2 +3 \(\le\) 3 với \(\forall\) x
=> -x2 + 4x -1 có thể không âm
=> sai đề
4)
-2x2 +6x -12
= -2(x2- 3x + 6)
= -2(x2 - 2.\(\dfrac{3}{2}\).x + \(\dfrac{9}{4}+\dfrac{15}{4}\))
= -2(x-\(\dfrac{3}{2}\))2 - \(\dfrac{15}{2}\) \(\le\) - \(\dfrac{15}{2}\) với \(\forall\) x
=> -2x2 +6x -12 luôn âm
=>đpcm
5)
6x2 +15x - 21
= 6(x2 + 2.\(\dfrac{15}{2}\)x + \(\dfrac{225}{4}\)- \(\dfrac{309}{4}\))
= 6.(x-\(\dfrac{15}{2}\))2 - \(\dfrac{927}{2}\) \(\ge\) - \(\dfrac{927}{2}\) với \(\forall\) x
=> 6x2 +15x - 21 có thể không âm
=> đề sai
mk làm lại ý 5. mk làm nhầm một chỗ
5)
6x2 +15x -21
= 6.(x2 + \(\dfrac{15}{6}\)x - \(\dfrac{21}{6}\))
= 6.(x2 + 2.\(\dfrac{5}{4}\).x + \(\dfrac{25}{16}\) - \(\dfrac{81}{16}\) )
= 6.(x + \(\dfrac{5}{4}\) )2 - \(\dfrac{243}{8}\) \(\ge\) - \(\dfrac{243}{8}\) với \(\forall\) x
=> 6x2 +15x -21 có thể không âm
=> đề sai
