Question

a) cho a/b=b/c=c/a và a+b+c khác 0; a=2005,Tính b,c.

b) Tính

9/10-1/90-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2

Answer 1

a)Ta có : \(a=2005\)

\(a+b+c\ne0\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}=\dfrac{2005}{b}+\dfrac{b}{c}+\dfrac{c}{2005}=\dfrac{2005+b+c}{b+c+2005}=1\)

\(\Rightarrow\dfrac{b}{2005}=1\Rightarrow b=2005\)

\(\Rightarrow\dfrac{c}{2005}=1\Rightarrow c=\dfrac{1}{2005}\)

Vậy .................................

Answer 2

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

\(\Rightarrow a = b = c\)

Mà \(a=2005\)

\(\Rightarrow b=c=2005\)

b) \(\dfrac{9}{10}-\dfrac{1}{90}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\)

\(=\dfrac{2268-28-36-45-60-84-126-210-420-1260}{2520}\)

\(=\dfrac{0}{2520}\)

\(=0\)

Answer 3

\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}\)

\(\Leftrightarrow=\dfrac{a+b+c}{b+c+a}\)(dựa vào t/c dãy tỉ số=nhau)

\(=1\)

\(\Leftrightarrow a=b=c=2005\)

\(\dfrac{9}{10}-\dfrac{1}{90}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\)

\(=0\)