a)Ta có: x2+x+1
=x2+2.x.1/2+1/4+3/4
=(x+1/2)2+3/4
Vì (x+1/2)2>=0 với mọi x
=>(x+1/2)2+3/4>0 với mọi x
Vậy x2+x+1>0 với mọi x.
b)Ta có: -5-x2+2x
=-(x2-2x+5)
=-(x2-2x+1+4)
=-(x-1)2-4
Ta có:(x-1)2>=0 với mọi x
=>-(x-1)2<=0 với mọi x
=>-(x-1)2-4<0 với mọi x
Vậy -5-x2+2x<0 với mọi x
a) x2+x+1 = \(x^2+\frac{1}{2}x+\frac{1}{2}x+\frac{1}{4}+\frac{3}{4}\)
= \(x\left(x+\frac{1}{2}\right)+\frac{1}{2}\left(x+\frac{1}{2}\right)+\frac{3}{4}\)
=\(\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\)
Do \(\left(x+\frac{1}{2}\right)^2\le0\)vs mọi x => \(\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)vs mọi x
=> x^2 + x + 1 > 0 vs mọi x
b) -5-x^2 + 2x = -(x^2 - 2x + 5) = \(-\left(x^2-2x+1+4\right)=-\left(x^2-2x+1\right)-4=-\left(x-1\right)^2-4\)
Do \(-\left(x-1\right)^2\le0\)vs mọi x=> \(-\left(x-1\right)^2-4< 0\)vs mọi x
=> -5-x^2+2x<0 vs mọi x