Question

Tìm số hữu tỉ x thỏa mãn (2x - 1)³ = 8/125 .

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Answer 1

\(\left(2x-1\right)^3=\dfrac{8}{125}\)

\(\left(2x-1\right)^3=\pm\left(\dfrac{2}{5}\right)^3\)

\(\text{Vậy }2x-1=\dfrac{2}{5}\)

       \(2x\)        \(=\dfrac{2}{5}+1=\dfrac{7}{5}\)

        \(x\)         \(=\dfrac{7}{5}.\dfrac{1}{2}=\dfrac{7}{10}\)

\(\text{hoặc }2x-1=\dfrac{-2}{5}\)

        \(2x\)        \(=\left(\dfrac{-2}{5}\right)+1=\dfrac{3}{5}\)

         \(x\)         \(=\dfrac{3}{5}.\dfrac{1}{2}=\dfrac{3}{10}\)

\(\Rightarrow x\in\left\{\dfrac{7}{10};\dfrac{3}{10}\right\}\)