Question

Tìm GTNN:

\(A=5\cdot\left|1-4x\right|-1\)

\(B=\left|x\right|+\left|x\right|\)

\(C=x^2+2\cdot\left|y-2\right|-1\)

Answer 1

A=5.|1-4x|-1

Do|1-4x|\(\ge0\Rightarrow5.\left|1-4x\right|\ge0\Rightarrow5.\left|1-4x\right|-1\ge\)-1

=>Min_A=-1

Dấu "=" xảy ra khi |1-4x|=0 <=> 1-4x=0 <=> x=\(\frac{1}{4}\)

b, B=|x|+|x|

Do|x|\(\ge0\Rightarrow\left|x\right|+\left|x\right|\ge0\)

=>Min _B=0 \(\Leftrightarrow\left|x\right|=0\Leftrightarrow x=0\)

c, C=x²+2.|y-2|-1

Do x²\(\ge0;2.\left|y-2\right|\ge0\Rightarrow x^2+2\left|y-2\right|\ge0\)

=>C\(\ge-1\)=> Min _C=-1

Dấu "=" xảy ra  khi \(\hept{\begin{cases}x^2=0\\\left|y-2\right|=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\y=2\end{cases}}}\)

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