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\(2017^0+\text{|}\frac{3}{5}-1\text{|}:\frac{4}{5}-\frac{5}{6}\)
\(=1+\text{|}\frac{3}{5}-\frac{5}{5}\text{|}:\frac{4}{5}-\frac{5}{6}\)
\(=1+\text{|}\frac{-2}{5}\text{|}:\frac{4}{5}-\frac{5}{6}\)
\(=1+\frac{2}{5}:\frac{4}{5}-\frac{5}{6}\)
\(=1+\frac{2}{5}.\frac{5}{4}-\frac{5}{6}\)
\(=1+\frac{1}{2}-\frac{5}{6}\)
\(=\frac{6}{6}+\frac{3}{6}-\frac{5}{6}\)
\(=\frac{4}{6}=\frac{2}{3}\)

a: \(=\dfrac{7+3}{6}\cdot\dfrac{1}{2}-2:\dfrac{7+3}{6}\)
\(=\dfrac{10}{12}-2\cdot\dfrac{6}{10}\)
\(=\dfrac{5}{6}-\dfrac{6}{5}=\dfrac{25-36}{30}=-\dfrac{11}{30}\)
b: \(=\left|\dfrac{10}{5}-\dfrac{2}{5}\right|\cdot\dfrac{1}{27}-\dfrac{3}{5}+1\)
\(=\dfrac{8}{5}\cdot\dfrac{1}{27}-\dfrac{3}{5}+1\)
\(=\dfrac{8}{135}-\dfrac{81}{135}+\dfrac{135}{135}=\dfrac{62}{135}\)

=> (x+2020)/5=(x+2020)/6=(x+2020)/3+(x+2020)/2
=>(x+2020)(1/5+1/6)=(x+2020)(1/3+1/2)
Với x+2020=0=>x=-2020
Với x+2020 khác 0=>1/5+1/6=1/3+1/2 ,vô lí
Vậy x=-2020

Bài 1 :
\(P\left(0\right)=d=2017\)
\(P\left(1\right)=a+b+c+d=2\Rightarrow a+b+c=-2015\)(*)
\(P\left(-1\right)=-a+b-c+d=6\Rightarrow-a+b-c=6-2017=-2023\)(**)
\(P\left(2\right)=8a+4b+2c+d=-6033\Rightarrow8a+4b+2c=-8050\)
Lấy (*) + (**) ta được : \(2b=-4038\Rightarrow b=-2019\)
Thay vào (*) ta được \(a+c=4\)(***)
Lại có : \(8a+4b+2c=-8050\Rightarrow8a+2c=-8050+8076=26\)(****)
(***) => \(8a+8c=32\)(*****)
Lấy (****) - (*****) => \(-6c=-6\Rightarrow c=1\Rightarrow a=3\)
Vậy ....

\(-\dfrac{1}{6}A=\left(-\dfrac{1}{6}\right)^1+\left(-\dfrac{1}{6}\right)^2+...+\left(-\dfrac{1}{6}\right)^{2018}\)
\(\Leftrightarrow-\dfrac{7}{6}A=\left(-\dfrac{1}{6}\right)^{2018}-\left(-\dfrac{1}{6}\right)^0=\dfrac{1}{6^{2018}}-1=\dfrac{1-6^{2018}}{6^{2018}}\)
\(\Leftrightarrow A=\dfrac{6^{2018}-1}{6^{2018}}:\dfrac{7}{6}=\dfrac{6^{2018}-1}{7\cdot6^{2017}}\)