Question

Cho: A = \(\dfrac{5}{17}+\dfrac{-4}{9}-\dfrac{20}{31}+\dfrac{12}{17}-\dfrac{11}{31}\)

và B = \(\dfrac{-3}{7}+\dfrac{7}{15}+\dfrac{-4}{7}+\dfrac{8}{15}-\dfrac{-2}{3}\)

1) Tính giá trị cỉa A và B

2) Tìm số nguyên x sao cho A< \(\dfrac{x}{9}\) \(\le\) B

Answer 1

\(\text{Câu 1 :}\)

\(A=\dfrac{5}{17}+\dfrac{-4}{9}-\dfrac{20}{31}+\dfrac{12}{17}-\dfrac{11}{31}\\ A=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)-\left(\dfrac{20}{31}+\dfrac{11}{31}\right)+\dfrac{-4}{9}\\ A=1-1+-\dfrac{4}{9}\\ A=-\dfrac{4}{9}\)

\(B=\dfrac{-3}{7}+\dfrac{7}{15}+\dfrac{-4}{7}+\dfrac{8}{15}-\dfrac{-2}{3}\\ B=\left(\dfrac{-3}{7}+\dfrac{-4}{7}\right)+\left(\dfrac{7}{15}+\dfrac{8}{18}\right)-\dfrac{-2}{3}\\ B=\left(-1\right)+1+\dfrac{2}{3}\\ B=\dfrac{2}{3}\)

\(\text{Câu 2 : }\)

\(A< \dfrac{x}{9}\le B\\ \Rightarrow\dfrac{-4}{9}< \dfrac{x}{9}\le\dfrac{2}{3}\\ \Rightarrow\dfrac{-4}{9}< \dfrac{x}{9}\le\dfrac{6}{9}\\ \Rightarrow-4< x\le6\\ \Rightarrow x\in\left\{\pm4;\pm3;\pm2;\pm1;0;5;6\right\}\)