Question

Nếu \(b>0,\) \(d>0\) thì từ \(\dfrac{a}{b}< \dfrac{c}{d}\) suy ra được: \(\dfrac{a}{b}< \dfrac{ab+cd}{b^2+d^2}< \dfrac{c}{d}\)

Answer 1

a/b<c/d

mà b>0 và d>0

nên \(\dfrac{a\cdot b}{b\cdot b}< \dfrac{c\cdot d}{d\cdot d}\)

=>ab/b^2<cd/d^2

=>\(\dfrac{ab}{b^2}< \dfrac{ab+cd}{b^2+d^2}< \dfrac{cd}{d^2}=\dfrac{c}{d}\)

=>\(\dfrac{a}{b}< \dfrac{ab+cd}{b^2+d^2}< \dfrac{c}{d}\)