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x2019-2019.x2018+2019.x2018+2019.x2017-2019.x2016+......2019.x-200 Tại x=2018
Giúp mik vs nhé
Sai đề nên t sửa luôn nhé!
Vì \(x=2018\Rightarrow2019=2018+1=x+1\)
\(A=x^{2017}-2019\cdot x^{2018}+2019\cdot x^{2017}-2019\cdot x^{2016}+....+2019\cdot x-200\)
\(\Rightarrow A=x^{2019}-\left(x+1\right)x^{2018}+\left(x+1\right)x^{2017}-\left(x+1\right)x^{2016}+....-\left(x+1\right)x^2+\left(x+1\right)x-200\)
\(\Rightarrow A=x^{2019}-x^{2019}-x^{2018}+x^{2018}+x^{2017}-x^{2017}-x^{2016}+....-x^3-x^2+x^2+x-200\)
\(\Rightarrow A=x-200=2018-200=1818\)
A= (10^2019+7)/(10^2019 + 1) = 1+ (6 / 10 ^2019+1)
B = ( 10 ^ 2020 +9) / ( 10 ^2020 +3) = 1 +( 6 / 10^ 2020 +3)
A -B = (6 / 10 ^2019+1) - (6 / 10^2020 +3) >0
=> A > B
Có \(\left(x-12\right)^{2018}\ge0\)
\(\left|y+1\right|^{2019}\ge0\)
\(\left(x-12\right)^{2018}+\left|y+1\right|^{2019}\ge0+0=0\)
Vậy Min = 0 <=> x = 12 ; y = -1
\(B=2019-\frac{2019}{3}-\frac{2019}{6}-\frac{2019}{10}-...-\frac{2019}{45}\)
\(\Leftrightarrow B=2019\left(1-\frac{1}{3}-\frac{1}{6}-\frac{1}{10}-...-\frac{1}{45}\right)\)
\(\Leftrightarrow B=2019\left[1-\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\right)\right]\)
\(\Leftrightarrow B=2019\left[1-\left(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{9.10}\right)\right]\)
\(\Leftrightarrow B=2019\left[1-2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\right]\)
\(\Leftrightarrow B=2019\left[1-2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\right]\)
\(\Leftrightarrow B=2019\left[1-2\left(\frac{1}{2}-\frac{1}{10}\right)\right]\)
\(\Leftrightarrow B=2019\left[1-2.\frac{4}{10}\right]\)
\(\Leftrightarrow B=2019\left[1-\frac{4}{5}\right]\)
\(\Leftrightarrow B=2019.\frac{1}{5}\)
\(\Leftrightarrow B=\frac{2019}{5}\)
\(\frac{x}{10}\)^2019+(0,1)^2019=\(\frac{1}{10}\)^2019 \(\frac{x}{10}\)^2019 =(0,1)^2019-(0,1)^2019 \(\frac{x}{10}\)^2019 =0 \(\frac{x}{10}\)^2019 =0^2019 \(\frac{x}{10}\) =0 x =0