Question

a, Cho a \(\ge\)3. Tìm min M= a + \(\dfrac{1}{a}\)

b, Cho a \(\ge\) 2. Tìm min N = a + \(\dfrac{1}{a^2}\)

Answer 1

\(M=\dfrac{a^2+1}{a}\Rightarrow M-\dfrac{10}{3}=\dfrac{a^2+1}{a}-\dfrac{10}{3}=\dfrac{3a^2-10a+3}{3a}=\dfrac{\left(3a-1\right)\left(a-3\right)}{3a}\)\(a\ge3\Rightarrow\left\{{}\begin{matrix}3a>0\\3a-1>0\\a-3\ge0\end{matrix}\right.\) \(\Rightarrow\dfrac{\left(3a-1\right)\left(a-3\right)}{3a}\ge0\)

\(\Rightarrow M-\dfrac{10}{3}\ge0\Rightarrow M\ge\dfrac{10}{3}\)

MIn M =10/3 khi x=3