Đáp án:
a) n²+5⋮n−2n+5⋮n−2
=n(n−2)+(2n+5)⋮n−2=n(n−2)+(2n+5)⋮n−2
Vì n(n−1)⋮n−2⇒2n+5⋮n−2n(n−1)⋮n−2⇒2n+5⋮n−2
⇒n−2+7⋮n−2⇒n−2+7⋮n−2
Vì n−2⋮n−2⇒7⋮n−2n−2⋮n−2⇒7⋮n−2
⇒n−2∈Ư(7)={±1;±7}⇒n−2∈Ư(7)={±1;±7}
⋅ n−2=−1⇒n=1· n−2=−1⇒n=1
⋅ n−2=1⇒n=3· n−2=1⇒n=3
⋅ n−2=−7⇒n=−5· n−2=−7⇒n=−5
⋅ n−2=7⇒n=9· n−2=7⇒n=9
b) 5n⋮n−15n⋮n−1
=5n−5+5⋮n−1=5n−5+5⋮n−1
=5(n−1)+5⋮n−1=5(n−1)+5⋮n−1
Vì 5(n−1)⋮n−1⇒5⋮n−15(n−1)⋮n−1⇒5⋮n−1
⇒n−1∈Ư(5)={±1;±5}⇒n−1∈Ư(5)={±1;±5}
⋅ n−1=−1⇒n=0· n−1=−1⇒n=0
⋅ n−1=1⇒n=2· n−1=1⇒n=2
⋅ n−1=−5⇒n=−4· n−1=−5⇒n=−4
⋅ n−1=5⇒n=6
