Question

bài 2. CM bỉu thức luôn âm

1. A= -x^2-2x-4

2. B= -x²-2x-3

3. C= -x^2-x-1

4. D= -2x^2 +6x-8

5. E=-2x^2-3x-4

Answer 1

1, \(A=-x^2-2x-4=-\left(x^2+2x+1+3\right)\)

\(=-\left(x+1\right)^2-3\le-3\)

\(\Rightarrow\)A luôn âm

2, tương tự

3, \(C=-x^2-x-1=-\left(x^2+2.x.\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{3}{4}\right)\)

\(=-\left(x+\dfrac{1}{2}\right)^2-\dfrac{3}{4}\le\dfrac{-3}{4}\)

\(\Rightarrow\)C luôn âm

4, \(D=-2x^2+6x-8=-2\left(x^2-3x+4\right)\)

\(=-2\left(x^2-\dfrac{3}{2}.x.2+\dfrac{9}{4}+\dfrac{7}{4}\right)\)

\(=-2\left(x-\dfrac{3}{2}\right)^2-\dfrac{7}{2}\le\dfrac{-7}{2}\)

\(\Rightarrow D\) luôn âm

5, tương tự