Question

[phan tú anh]

Tìm n,m thuộc Z :1/m+n/6=1/2

Answer 1

[Akai Haruma]

Lời giải:

$\frac{1}{m}+\frac{n}{6}=\frac{1}{2}$

$\Rightarrow \frac{mn+6}{6m}=\frac{1}{2}=\frac{3m}{6m}$

$\Rightarrow mn+6=3m$

$\Rightarrow m(n-3)=-6$

Do $m,n$ nguyên nên ta xét các TH sau:

TH1: $m=1, n-3=-6\Rightarrow m=1; n=3$

TH2: $m=-1, n-3=6\Rightarrow m=-1; n=9$

TH3: $m=2, n-3=-3\Rightarrow m=2; n=0$

TH4: $m=-2, n-3=3\Rightarrow m=-2; n=6$

TH5: $m=3, n-3=-2\Rightarrow m=3; n=1$

TH6: $m=-3, n-3=2\Rightarrow m=-3; n=5$

TH7: $m=6, n-3=-1\Rightarrow m=6; n=2$

TH8: $m=-6, n-3=1\Rightarrow m=-6; n=4$