Bài 8. Tìm số nguyên x \(\inℕ^∗\), biết:
\(a\text{)}\dfrac{6}{x}< \dfrac{x}{7}< \dfrac{8}{x}\)
\(b\text{)}\dfrac{x}{11}< \dfrac{12}{x}< \dfrac{x}{9}\)
\(c\text{)}\dfrac{4}{x}< \dfrac{x}{8}< \dfrac{5}{x}\)
\(d\text{)}\dfrac{x}{9}< \dfrac{8}{x}< \dfrac{x}{7}\)
a; \(\dfrac{6}{x}\) < \(\dfrac{x}{7}\) < \(\dfrac{8}{x}\)
vì \(x\) \(\in\) N* ta có: 6.7 < \(x.x\) < 7.8
42 < \(x^2\) < 56
\(x^2\) = 49
\(x\) = \(\pm\) 7
Vì \(x\) \(\in\) N*; \(x\) = 7
b; \(\dfrac{x}{11}\) < \(\dfrac{12}{x}\) < \(\dfrac{x}{9}\)
9.12< \(x^2\) < 11.12
108 < \(x^2\) < 132
\(x^2\) = 121
\(\left[{}\begin{matrix}x=-11\\x=11\end{matrix}\right.\)
Vì \(x\in\) N*
\(x\) = 11