Question

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giúp em với ạ 

Answer 1

[Member lỗi thời :>>]

Bài 72 :

a) Vì \(\left|2x-\frac{1}{3}\right|\ge0\forall x\)

\(\Rightarrow\left|2x-\frac{1}{3}\right|-\frac{7}{4}\ge-\frac{7}{4}\forall x\)

\(\Rightarrow A\ge-\frac{7}{4}\)

Dấu "=" xảy ra <=> \(\left|2x-\frac{1}{3}\right|=0\)

\(\Leftrightarrow2x-\frac{1}{3}=0\Leftrightarrow2x=\frac{1}{3}\Leftrightarrow x=\frac{1}{6}\)

b) Vì \(\hept{\begin{cases}\frac{1}{3}\left|x-2\right|\ge0∀x\\2\left|3-\frac{1}{2}y\right|\ge0∀y\end{cases}}\)\(\Rightarrow\frac{1}{3}\left|x-2\right|+2\left|3-\frac{1}{2}y\right|+4\ge4∀y\)

=> B ≥ 4

Dấu "=" xảy ra <=> \(\hept{\begin{cases}\left|x-2\right|=0\\\left|3-\frac{1}{2}y\right|=0\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x-2=0\\3-\frac{1}{2}y=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=2\\\frac{1}{2}y=3\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x=2\\y=6\end{cases}}\)

Answer 2

[Member lỗi thời :&gt;&gt;]

Bài 73 :

a) Vì | 1 + 2x | ≥ 0 ∀ x

\(\Rightarrow\frac{1}{4}\left|1+2x\right|\ge0\forall x\)

\(\Rightarrow2,25-\frac{1}{4}\left|1+2x\right|\le2,25\forall x\)

=> A ≤ 2,25

Dấu "=" xảy ra <=> | 1 + 2x | = 0 <=> 1 + 2x = 0 <=> 2x = -1 <=> \(x=\frac{-1}{2}\)

b) Vì | 2x - 3 | ≥ 0 ∀ x

\(\Rightarrow\frac{1}{2}\left|2x-3\right|\ge0\forall x\)

\(\Rightarrow3+\frac{1}{2}\left|2x-3\right|\ge3\forall x\)

\(\Rightarrow\frac{1}{3+\frac{1}{2}\left|2x-3\right|}\le\frac{1}{3}\forall x\)

\(\Rightarrow B\le\frac{1}{3}\)

Dấu "=" xảy ra <=> | 2x - 3 | = 0 <=> 2x - 3 = 0 <=> 2x = 3 \(\Leftrightarrow x=\frac{3}{2}\)