Question

b)Tìm các số nguyên sao cho-7x-11    chia hết cho 2x+4

Answer 1

Ta có : −7.x−11⋮2x+4−7.x−11⋮2x+4

=) [−7.x−11+(2x+4)]⋮2x+4[−7.x−11+(2x+4)]⋮2x+4

=)  2[−7x−11+7(2.x+4)]⋮2.x+42[−7x−11+7(2.x+4)]⋮2.x+4

=) [−14.x−22+(14.x+28)]⋮2.x+4[−14.x−22+(14.x+28)]⋮2.x+4

=) −14.x−22+14.x+28⋮2.x+4−14.x−22+14.x+28⋮2.x+4

=) (−14.x+14.x)+(−22+28)⋮2.x+4(−14.x+14.x)+(−22+28)⋮2.x+4

=) 6⋮2.x+46⋮2.x+4

=) 2.x+4∈Ư(6)={+−1;+−2;+−3;+−6}2.x+4∈Ư(6)={+−1;+−2;+−3;+−6}

=)