حل (b-d)(d-c)(d-a)<0.(b-d)(b-a)(a-c)<0.(b-d)(d-c)(a-c)<0

$$( b - d ) ( d - c ) ( d - a ) < 0 . ( b - d ) ( b - a ) ( a - c ) < 0 . ( b - d ) ( d - c ) ( a - c ) < 0$$

برای d حل کنید

$$\left\{\begin{matrix}d\in \left(a,c\right)\text{, }&c>a\text{ and }b>c\\d\in \left(a,b\right)\text{, }&b>a\text{ and }b\leq c\\d\in \left(c,b\right)\text{, }&b>c\text{ and }b\leq a\\d\in \left(c,a\right)\text{, }&b>a\text{ and }c<a\\d>b\text{, }&b\geq a\text{ and }b\geq c\\d>c\text{, }&c\geq a\text{ and }b<c\\d>a\text{, }&\left(b\geq c\text{ and }b<a\right)\text{ or }\left(c<a\text{ and }b<c\right)\\d\in \left(b,c\right)\text{, }&c\leq a\text{ and }b<c\\d\in \left(b,a\right)\text{, }&c>a\text{ and }b<a\end{matrix}\right.$$

برای c حل کنید

$$\left\{\begin{matrix}c>d\text{, }&\left(b<d\text{ and }d<a\right)\text{ or }\left(b>d\text{ and }d>a\right)\\c<d\text{, }&\left(d>a\text{ and }b<d\right)\text{ or }\left(b>d\text{ and }d<a\right)\end{matrix}\right.$$