Question

Tìm số nguyên x biết: \(\frac{\sqrt{49}}{6}< Ix-\frac{2}{3}I< \frac{26}{\sqrt{81}}\)

Answer 1

- Ta có : \(\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\)

=> \(\left\{{}\begin{matrix}\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|\\\left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}\frac{7}{6}< \left|x-\frac{2}{3}\right|\\\left|x-\frac{2}{3}\right|< \frac{26}{9}\end{matrix}\right.\)

- TH₁ : \(x-\frac{2}{3}\ge0\left(x\ge\frac{2}{3}\right)\)

=> \(\left\{{}\begin{matrix}\frac{7}{6}< x-\frac{2}{3}\\x-\frac{2}{3}< \frac{26}{9}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}\frac{11}{6}< x\\x< \frac{32}{9}\end{matrix}\right.\)

=> \(\frac{11}{6}< x< \frac{32}{9}\)

Mà x là số nguyên .

=> \(x\in\left\{2,3\right\}\)

- TH₂ : \(x-\frac{2}{3}< 0\left(x< \frac{2}{3}\right)\)

=> \(\left\{{}\begin{matrix}\frac{7}{6}< \frac{2}{3}-x\\\frac{2}{3}-x< \frac{26}{9}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}\frac{1}{2}< -x\\-x< \frac{20}{9}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}-\frac{1}{2}>x\\x>-\frac{20}{9}\end{matrix}\right.\)

=> \(-\frac{1}{2}>x>-\frac{20}{9}\)

Mà x là số nguyên .

=> \(x\in\left\{-1,-2\right\}\)

Answer 2

I là tham số à bạn