Toán Lớp 8: tìm giá trị để P=3x-1/2x+2 nguyên

Question

Toán Lớp 8:  tìm giá trị để P=3x-1/2x+2 nguyên

bichquyenlien · Answer

Để  P in Z  th&igrave;:    (3x - 1)  vdots (2x + 2)    (ĐK: x ne -1)    => (6x - 2)  vdots (2x + 2)     => (6x + 6 - 8)  vdots (2x + 2)    V&igrave;  (6x + 6)  vdots (2x + 2)     => -8  vdots (2x + 2)     => (2x + 2) in Ư(-8) = {&plusmn;1 ; &plusmn;2 ; &plusmn;4 ; &plusmn;8}    $ begin{array}{|c|c|c|} hline 2x+2&-8&-4&-2&-1&1&2&4&8   hline 2x&-10&-6&-4&-3&-1&0&2&6   hline x&-5&-3&-2&- frac{3}{2}&- frac{1}{2}&0&1&3   hline &tm&tm&tm&tm&tm&tm&tm&tm   hline  end{array}$   Vậy  x in {-5 ; -3 ; -2 ; -3/2 ; -1/2 ; 0 ; 1 ; 3}  th&igrave;  P in Z

hoquyly · Answer

Ta c&oacute;:   $P= dfrac{3x-1}{2x+2}$   $P= dfrac{6x-2}{2x+2}$   $P= dfrac{6x+6-8}{2x+2}$   $P= dfrac{3(2x+2)-8}{2x+2}$   $P=3- dfrac{8}{2x+2}$   Để $P$ l&agrave; số nguy&ecirc;n th&igrave; $8 ; vdots ; 2x+2$   $&hArr; 2x+2  in Ư(8)= { pm 1;  pm 2; pm 4;  pm 8 }$   $&hArr; 2x in  {-1;-3;0;-4;2;-6;1;-10 }$   $&hArr; x in  {0;-2;1;-3;-5 }$