Đáp án + giải thích bước giải :
$1/$ `|2x - 5| - |3x - 2| = 0`
`⇔ |2x - 5| = 0 + |3x - 2|`
`⇔ |2x - 5| = |3x - 2|`
`⇔` \(\left[ \begin{array}{l}2x-5=3x-2\\2x-5=-3x+2\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}2x - 3x = 5 - 2\\2x+3x=5+2\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}-x = 3\\5x=7\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x = -3\\x=\frac{7}{5}\end{array} \right.\)
Vậy `x ∈ {-3; 7/5}`
$2/$
Gọi $ULCN (5n + 2; 2n + 1) = d$
`⇔` \(\left\{ \begin{array}{l}5n+2\vdots d\\2n+1\vdots d \end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}2 (5n+2)\vdots d\\5(2n+1)\vdots d \end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}10n+4\vdots d\\10n+5\vdots d \end{array} \right.\)
`⇔ (10n + 4) - (10n + 5) \vdots d`
`⇔ 10n + 4 - 10n - 5 \vdots d`
`⇔ -1 \vdots d`
`⇔ d ∈ Ư (-1) = {±1}`
`-> (5n + 2)/(2n + 1)` là phân số tối giản
