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0,(57)=0,(01).57 = \(\frac{1}{99}.57=\frac{19}{33}\)
0,(42)=0,(01).42=\(\frac{1}{99}.42=\frac{14}{33}\)
=>0,(57)+0,(42)=\(\frac{19}{33}+\frac{14}{33}=\frac{33}{33}=1\)
Vậy 0,(57)+0,)42)=1
a) 0,(5)+0,(3)+0,(1)
=\(\frac{5}{9}\)+\(\frac{1}{3}\)+\(\frac{1}{9}\)
=\(\frac{5}{9}\)+\(\frac{3}{9}\)+\(\frac{1}{9}\)
=\(\frac{5+3+1}{9}\)
=\(\frac{9}{9}\)
=1
b) 0,(57)+0,(42)
=\(\frac{19}{33}\)+\(\frac{14}{33}\)
=\(\frac{19+14}{33}\)
=\(\frac{33}{33}\)
=1
Chúc cậu học tốt •ω•
x/2 + x/4 + x/2016 = x/3 + x/5 + x/2017
=> x/2 + x/4 + x/2016 - x/3 - x/5 - x/2017 = 0
=> x.(1/2 + 1/4 + 1/2016 - 1/3 - 1/5 - 1/2017) = 0
Vì 1/2 > 1/3; 1/4 > 1/5; 1/2016 > 1/2017
=> 1/2 + 1/4 + 1/2016 - 1/3 - 1/5 - 1/2017 khác 0
=> x = 0
Ta có:
\(\frac{x}{2}+\frac{x}{4}+\frac{x}{2016}=\frac{x}{3}+\frac{x}{5}+\frac{x}{2017}\)
=>\(\frac{x}{2}+\frac{x}{4}+\frac{x}{2016}-\frac{x}{3}-\frac{x}{5}-\frac{x}{2017}=0\)
=>\(x.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{2016}-\frac{1}{3}-\frac{1}{5}-\frac{1}{2017}\right)=0\)
áp dụng t/c : A.B=0 =>hoặc A=0 hoặc B=0 ta có:
Vì \(\frac{1}{2}+\frac{1}{4}+\frac{1}{2016}-\frac{1}{3}-\frac{1}{5}-\frac{1}{2017}\ne0\)
=>x=0
a: \(\dfrac{2032-x}{25}+\dfrac{2053-x}{23}+\dfrac{2070-x}{21}+\dfrac{2083-x}{19}-10=0\)
\(\Leftrightarrow\left(\dfrac{2032-x}{25}-1\right)+\left(\dfrac{2053-x}{23}-2\right)+\left(\dfrac{2070-x}{21}-3\right)+\left(\dfrac{2083-x}{19}-4\right)=0\)
=>2007-x=0
hay x=2007
b: \(\Leftrightarrow x+\left(1+1+1+1+1+1+1\right)+\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)=0\)
\(\Leftrightarrow x+7+\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)=0\)
=>x+7+1/3-1/10=0
hay x=-217/30