Question

tim gtnn cua: can x^-2x+1 +can x^+6x+9

Answer 1

\(\sqrt{x^2-2x+1}+\sqrt{x^2+6x+9}=\sqrt{\left(x-1\right)^2}+\sqrt{\left(x+3\right)^2}\\ =\left|x-1\right|+\left|x+3\right|\\ =\left|x+3\right|+\left|-x+1\right|>=\left|x+3-x+1\right|=\left|4\right|=4\\ \)

\(Dấu\ ''=''\ xảy\ ra \ khi : \) \(\left(x+3\right)\left(-x+1\right)\ge0< =>\left(x+3\right)\left(x-1\right)\le0\\ =>\left\{{}\begin{matrix}x+3\ge0\\x-1\le0\end{matrix}\right.< =>-3\le x\le1\)

\(Vậy \ GTNN \ của \ biểu \ thức \ trên \ là : 4\ khi\ -3=<\ x\ =<1\)