Question

[Trâm Nguyễn]

tìm số nguyên a sao cho:

a) 2/3 < a-1/6 < 8/9

d) 12/9 < 4/a < 8/3

Answer 1

[Dang Tung]

a) \(\dfrac{2}{3}< a-\dfrac{1}{6}< \dfrac{8}{9}\\ \Rightarrow\dfrac{2}{3}+\dfrac{1}{6}< a-\dfrac{1}{6}+\dfrac{1}{6}< \dfrac{8}{9}+\dfrac{1}{6}\\ \dfrac{5}{6}< a< \dfrac{19}{18}\)

Do a là số nguyên nên a=1

b) \(\dfrac{12}{9}< \dfrac{4}{a}< \dfrac{8}{3}\left(a\ne0\right)\\ \Rightarrow\dfrac{4}{3}< \dfrac{4}{a}< \dfrac{4}{\dfrac{3}{2}}\\ \Rightarrow3>a>1,5\)

Do a là số nguyên nên a=2

Answer 2

[Nguyễn Lê Phước Thịnh]

a: \(\dfrac{2}{3}< \dfrac{a-1}{6}< \dfrac{8}{9}\)

=>\(\dfrac{12}{18}< \dfrac{3\left(a-1\right)}{18}< \dfrac{16}{18}\)

=>12<3(a-1)<16

=>12<3a-3<16

=>15<3a<19

=>\(5< a< \dfrac{19}{3}\)

mà a nguyên

nên a=6

b: \(\dfrac{12}{9}< \dfrac{4}{a}< \dfrac{8}{3}\)

=>\(\dfrac{24}{18}< \dfrac{24}{6a}< \dfrac{24}{9}\)

=>9<6a<18

mà a nguyên

nên 6a=12

=>a=2