Question

Gíup mình nha

a)Tìm x :

\((\dfrac{3}{14}x-1).2\dfrac{1}{3}=-\dfrac{1}{6}\)

b)Chứng tỏ

\((1-\dfrac{1}{2}).(1-\dfrac{1}{3})...(1-\dfrac{1}{10})< \dfrac{1}{2}\)

Answer 1

a) \(\left(\dfrac{3}{14}x-1\right).2\dfrac{1}{3}=-\dfrac{1}{6}\)

\(\left(\dfrac{3}{14}x-1\right)=-\dfrac{1}{6}:\dfrac{7}{3}\)

\(\dfrac{3}{14}x-1=-\dfrac{1}{14}\)

\(\dfrac{3}{14}x=-\dfrac{1}{14}+1\)

\(x=\dfrac{13}{14}:\dfrac{3}{14}\)

\(x=\dfrac{13}{3}\)

Answer 2

b) Gọi biểu thức trên là A

\(A=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right)...\left(1-\dfrac{1}{10}\right)\)

\(A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{9}{10}=\dfrac{1.2.3...9}{2.3.4...10}=\dfrac{1}{10}\)

Vì \(\dfrac{1}{10}< \dfrac{1}{2}\) \(\Rightarrow A< \dfrac{1}{2}\)