Khó thế
làm thôi chứ mình nghĩ quá với lớp 6
\(\left\{{}\begin{matrix}\dfrac{4}{7}< \dfrac{a}{b}< \dfrac{2}{3}\\7a+4b=1994\end{matrix}\right.\)
\(7a+4b=1994\Rightarrow a=\dfrac{1994-4b}{7}=\dfrac{1998-4-4b}{7}\)
\(\Rightarrow\left\{{}\begin{matrix}b=7n-2\\a=286-4n\end{matrix}\right.\)(*)
\(\left\{{}\begin{matrix}\dfrac{a}{b}< \dfrac{2}{3}\left(1\right)\\\dfrac{a}{b}>\dfrac{4}{7}\left(2\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow3a< 2b\Rightarrow3\left(286-4n\right)< 2\left(7n-2\right)\)
\(858-12n< 14n-4\Rightarrow n>\dfrac{862}{26}=33,15..\)
\(\left(2\right)\Leftrightarrow7a>4b\Rightarrow7\left(286-4n\right)>2\left(7n-2\right)\)
\(\Leftrightarrow1932-28n>14n-4\Rightarrow N< \dfrac{1936}{42}=46,09..\)
\(\)Tập hợp giá trị phân số a/b thỏa mãn là:
\(\left\{{}\begin{matrix}n\in N\\33< n\le46\\\dfrac{a}{b}=\dfrac{286-4n}{7n-2}\end{matrix}\right.\)
thích bao nhiêu thay vào
ví dụ
\(\left\{{}\begin{matrix}n=34\\\dfrac{a}{b}=\dfrac{286-4.34}{7.34-2}=\dfrac{150}{236}\\7.150+4.236=1050+944=1994\end{matrix}\right.\)
