Question

Chứng minh rằng:
1)  A=x^2 + 2x + 2 >0
2)   B= -4x^2  +  4x  - 2<0

Answer 1

`1)A=x^2+2x+2`

`A=x^2+2x+1=(x+1)^2+1>=1>0(dpcm)`

`2)B=-4x^2+4x-2`

`B=-4x^2+4x-1-1=-(2x-1)^2-1<=-1<0(dpcm)`

Answer 2

1. Ta có \(A=x^2+2x+2=\left(x+1\right)^2+1\)

mà \(\left(x+1\right)^2\ge0\forall x\Rightarrow\left(x+1\right)^2+1\ge1>0\)

\(\Rightarrow A=x^2+2x+2>0\) ( đpcm ) 

2. Ta có \(B=-4x^2+4x-2=-\left(4x^2-4x+2\right)=-\left[\left(2x-1\right)^2+1\right]\)

mà \(\left(2x-1\right)^2\ge0\forall x\Rightarrow\left(2x-1\right)^2+1\ge1\Rightarrow-\left[\left(2x-1\right)^2+1\right]\le-1< 0\)

\(\Rightarrow B=-4x^2+4x-2< 0\) ( đpcm )