Question

Answer 1

\(x^2+6x+10=\left(x+3\right)^2+1\)

Do \(\left\{{}\begin{matrix}\left(x+3\right)^2\ge0;\forall x\\1>0\end{matrix}\right.\) \(\Rightarrow\left(x+3\right)^2+1>0\) ;\(\forall x\)

\(4x-x^2-5=-\left(x-2\right)^2-1\)

Do \(\left\{{}\begin{matrix}-\left(x-2\right)^2\le0;\forall x\\-1< 0\end{matrix}\right.\) \(\Rightarrow-\left(x-2\right)^2-1< 0;\forall x\)

Answer 2

`a, x^2 - 6x + 10 = x^2 - 6x + 9 + 1 = (x-3)^2 + 1 >= 0 + 1 = 1 > 0 forall x in RR`

`b, -(x^2 - 4x + 5) = -(x^2 - 4x + 4) - 1 < 0 - 1 =- 1 < 0 forall x in RR`