Question

При каких значениях параметра b уравнение 5x/6-b=1/3 имеет: а) положительные корень б) корень, принадлежащий промежутку (-1; 4)

Answer 1

$\frac{5x}{6}-b=\frac{1}{3}, \\ \frac{5x}{6}=b+\frac{1}{3}, \\ x=\frac{6b}{5}+\frac{2}{5}; \\ 1) \ x\ \textgreater \ 0, \ \frac{6b}{5}+\frac{2}{5}\ \textgreater \ 0, \\ \frac{6b}{5}\ \textgreater \ -\frac{2}{5}, \\ b\ \textgreater \ -\frac{1}{3}; \\ 2) \ -1\ \textless \ x\ \textless \ 4, \ -1\ \textless \ \frac{6b}{5}+\frac{2}{5}\ \textless \ 4, \\ -1-\frac{2}{5}\ \textless \ \frac{6b}{5}\ \textless \ 4-\frac{2}{5}, \\ -\frac{7}{5}\ \textless \ \frac{6b}{5}\ \textless \ \frac{18}{5}, \\ -\frac{7}{6}\ \textless \ b\ \textless \ 3.$