13 tháng 8 2021 lúc 15:03
\(A=\left|5x+3\right|+\left|4x-5\right|+5=\dfrac{5}{4}\left|4x+\dfrac{12}{5}\right|+\left|5-4x\right|+5\)
\(A=\dfrac{1}{4}\left|4x+\dfrac{12}{5}\right|+\left|4x+\dfrac{12}{5}\right|+\left|5-4x\right|+5\)
\(A\ge\dfrac{1}{4}\left|4x+\dfrac{12}{5}\right|+\left|4x+\dfrac{12}{5}+5-4x\right|+5=\dfrac{1}{4}\left|4x+\dfrac{12}{5}\right|+\dfrac{62}{5}\ge\dfrac{62}{5}\)
\(A_{min}=\dfrac{62}{5}\) khi \(x=-\dfrac{3}{5}\)
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