Question

cho a,b,c,d\(\in\)N* thỏa mãn \(\frac{a}{b}\)<\(\frac{c}{d}\).

Chứng tỏ rằng :\(\frac{2002a+c}{2002b+d}\)<\(\frac{c}{d}\)

Answer 1

Vì \(\frac{a}{b}< \frac{c}{d}\Rightarrow\frac{a}{b}.bd< \frac{c}{d}.bd\)

\(\Rightarrow ad< bc\)

\(\Rightarrow2002ad< 2002bc\)

\(\Rightarrow2002ad+cd< 2002bc+cd\)

\(\Rightarrow\left(2002a+c\right).d< \left(2002b+d\right).c\)

Chia cả hai vế cho \(\left(2002b+d\right).d\) ta có :

\(\frac{2002a+c}{2002b+d}< \frac{c}{d}\)

Vậy...

Answer 2

Vì \(\frac{a}{b}< \frac{c}{d}\)

\(\Rightarrow ad< bc\)

\(\Rightarrow2002ad< 2002bc\)

\(\Rightarrow2002ad+cd< 2002bc+cd\)

\(\Rightarrow\left(2002a+c\right)d< \left(2002b+d\right)c\)

\(\Rightarrow\frac{2002a+c}{2002b+d}< \frac{c}{d}\)

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Answer 3

mong các bạn ủng hộ cho mình

Answer 4

\(\frac{2002a+c}{2002b+d}< \frac{c}{d}\)

\(\Leftrightarrow\left(2002a+c\right).d< c.\left(2002b+d\right)\)

\(\Leftrightarrow2002ad+cd< 2002bc+cd\)

\(\Leftrightarrow2002ad< 2002bc\)

\(\Leftrightarrow ad< bc\)

\(\Rightarrow\frac{a}{b}< \frac{c}{d}\) (luôn đúng)