Question

tìm các số nguyên x để

\(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)

Answer 1

Có 1/3+3/35=44/105

Có 4/7+3/5+1/3=158/105

=> 44/105< x/210<158/105         MC: 210

=> 88/210< x/210< 316/210

Vậy x thuộc {89;90;91;92;...;315}

Answer 2

Ta có : 

\(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)

\(\Leftrightarrow\)\(\frac{70}{210}+\frac{18}{210}< \frac{x}{210}< \frac{120}{210}+\frac{126}{210}+\frac{70}{210}\)

\(\Leftrightarrow\)\(\frac{70+18}{210}< \frac{x}{210}< \frac{120+126+70}{210}\)

\(\Leftrightarrow\)\(\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)

\(\Leftrightarrow\)\(88< x< 316\)

\(\Rightarrow\)\(x\in\left\{89;90;91;...;314;315\right\}\)

Vậy \(x\in\left\{89;90;91;...;314;315\right\}\)

Chúc bạn học tốt ~