Question

Answer 1

`A=[4x^4+1]/[2x^2-2x+1]`

`A=[4x^4+4x^2+1-4x^2]/[2x^2-2x+1]`

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

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

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

`=>N(x)=2x^2+2x+1`

`=>N(x)=2(x^2+x+1/2)`

`=>N(x)=2(x+1/2)^2+1/2`

Vì `2(x+1/2)^2 >= 0<=>2(x+1/2)^2+1/2 >= 1/2`

   `=>N(x) >= 0,5`

`=>GTN N` của `N(x)` là `0,5`

Answer 2

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

N(x)=2x^2+2x+1

=2(x^2+x+1/2)

=2(x^2+x+1/4+1/4)

=2(x+1/2)^2+1/2>=1/2

Dấu = xảy ra khi x=-1/2