Đáp án:
\(m=4\)
Giải thích các bước giải:
$$\eqalign{
& f\left( x \right) = {x^4} - 2m{x^2} + m \cr
& f'\left( x \right) = 4{x^3} - 4mx = 0 \Leftrightarrow 4x\left( {{x^2} - m} \right) = 0 \cr
& \Leftrightarrow \left[ \matrix{
x = 0 \hfill \cr
{x^2} = m \hfill \cr} \right. \cr
& De\,ham\,so\,\,co\,\,cuc\,\,dai \Rightarrow pt\,\,{x^2} = m\,\,co\,\,2\,\,nghiem\,\,pb\,\,khac\,\,0 \cr
& \Leftrightarrow m > 0 \cr
& f'\left( x \right) = 0 \Leftrightarrow \left[ \matrix{
x = 0 \hfill \cr
x = - \sqrt m \hfill \cr
x = \sqrt m \hfill \cr} \right. \cr
& Lap\,BBT \Rightarrow Ham\,\,so\,\,dat\,\,cuc\,\,dai\,\,tai\,\,x = 0 \cr
& \Rightarrow Diem\,\,cuc\,\,dai\,\,A\left( {0;m} \right) \cr
& A \in Duong\,\,tron\,\,tam\,\,I\left( {3;0} \right),\,\,ban\,\,kinh\,\,r = 5 \cr
& \Leftrightarrow IA = 5 \cr
& \Leftrightarrow {\left( {0 - 3} \right)^2} + {\left( {m - 0} \right)^2} = 25 \cr
& \Leftrightarrow {m^2} = 16 \Leftrightarrow m = \pm 4 \cr
& Ket\,\,hop\,\,DK \Rightarrow m = 4 \cr} $$
