Question

cm 4x-x^2-5 < 0

Answer 1

Ta có: \(-x^2+4x-5=-\left(x^2-4x+4\right)-1=-\left(x-2\right)^2-1\le-1< 0\forall x\in R\)

 

Answer 2

`4x-x^2-5`

`=-(x^2-4x+5)`

`=-[(x^2-4x+4)+1]`

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

Ta thấy `-(x-2)^2<=0,∀x`

`->-(x-2)^2-1<=-1<0,∀x` ( đpcm )

 

Answer 3

Ta có: \(-x^2+4x-5\)

\(=-\left(x^2-4x+5\right)\)

\(=-\left(x-2\right)^2-1< 0\forall x\)