Question

cho hai so huu ti a/b va c/d voi mau duong, trong do a/b < c/d . chung minh rang :

a . ad < bc                                          b . a/b < a+c / b+d < c/d

giup mk nha 

Answer 1

a, Vì b,d > 0 -> ad/bd < cb/bd -> ad<bc
b, ad<bc -> ad/bd < bc/bd ( vì b,d > 0 => bd>0) => a/b < c/d

Answer 2

a) \(\frac{a}{b}< \frac{c}{d}\Rightarrow ad< bc\)

b) \(ad< bc\Leftrightarrow ad+ab< bc+ab\)

\(\Leftrightarrow a\left(b+d\right)< b\left(a+c\right)\)

\(\Leftrightarrow\frac{a}{b}< \frac{a+c}{b+d}\) (1)

\(ad< bc\Leftrightarrow ad+cd< bc+cd\)

\(\Leftrightarrow d\left(a+c\right)< c\left(b+d\right)\)

\(\Leftrightarrow\frac{a+c}{b+d}< \frac{c}{d}\) (2)

Từ (1) và (2) suy ra: \(\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}\)