Question

gia tri nho nhat cua da thuc f(x)= lx-2l + lx-3l + lx-6l

Answer 1

Vì \(\left|x-2\right|\ge0\)

     \(\left|x-3\right|\ge0\)

     \(\left|x-6\right|\ge0\)

             Do đó:\(\left|x-2\right|+\left|x-3\right|+\left|x-6\right|\ge0\)

Dấu = xảy ra khi \(\hept{\begin{cases}x-2=0\\x-3=0\\x-6=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=2\\x=3\\x=6\end{cases}}\)

                               Vậy Min F(x)=0 khi x=2;3;6

Answer 2

f(x)=|x-2|+|x-3|+|x-6| >= |2-x+x-6|=|-4|=4 (bđt |a|+|b| >= |a+b|)

dấu "=" xảy ra <=> (2-x)(x-6) >= 0 <=>2 <=x <= 6