Question

1.Cho a,b,c \(\in N\)

CMR:a, 1<\(\dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< 2\)

b, \(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\ge\dfrac{3}{2}\)

Mn giúp mk vs nak!!!!

Thks nhìu!!!

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Answer 1

a, Ta có: \(\dfrac{a}{a+b+c}< \dfrac{a}{a+b}< \dfrac{a+c}{a+b+c}\) (1)

\(\dfrac{b}{a+b+c}< \dfrac{b}{b+c}< \dfrac{b+a}{a+b+c}\) (1)

\(\dfrac{c}{a+b+c}< \dfrac{c}{c+a}< \dfrac{c+b}{a+b+c}\) (3)

Từ (1), (2), (3) \(\Rightarrow\dfrac{a}{a+b+c}+\dfrac{b}{a+b+c}+\dfrac{c}{a+b+c}< \dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< \dfrac{a+c}{a+b+c}+\dfrac{b+a}{a+b+c}+\dfrac{c+b}{a+b+c}\Rightarrow1< \dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< 2\)

Thầy mk hướng dẫn phần a như thế còn phần b mk ko bt lm, chúc p hk tốt