Đáp án:
Giải thích các bước giải:
a,
$A$∈Z⇔$\dfrac{5n+13}{3n+7}$ $∈Z$⇔$5n+13$ $\vdots$ $3n+7$
⇔$3(5n+13)$$\vdots$ $3n+7$
⇔$15n+39$$\vdots$ $3n+7$
⇔$15n+35+4$$\vdots$ $3n+7$
⇔$5(3n+7)+4$$\vdots$ $3n+7$
Mà $5.3n+7$$\vdots$ $3n+7$
⇒$4$$\vdots$ $3n+7$
⇒$3n+7∈Ư(4)=${$1,-1,2,-2,4,-4$}
⇒$n∈${$-2,-8/3,-3,-1.-11/3$}
⇒$n=-2,-3,-1$
b,
Ta có: $\dfrac{5n+13}{3n+7}$ $Max$⇔$\dfrac{5/3(3n+7)+4/3}{3+7}$ $Max$⇔$5/3+$ $\dfrac{4/3}{3n+7}$$Max$ ⇔$3n+7 Max$⇔$3n+7=1$⇔$n=-2$