a=\(\frac{-7}{2018^{2019}}\)+ \(\frac{-15}{2018^{2018}}\)
b= \(\frac{-15}{2018^{2019}}\)+ \(\frac{-7}{2018^{2018}}\)
mk cần gấp nha
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\(-\frac{2018}{2019}.\frac{2}{7}-\frac{2018}{2019}.\frac{5}{7}+1\frac{2018}{2019}=\frac{2018}{2019}\left(\frac{-2-5}{7}\right)+1\frac{2018}{2019}=\frac{2018}{2019}.\left(-1\right)+1\frac{2018}{2019}=\frac{-2018}{2019}+1\frac{2018}{2019}=1\)
=2018.2018/2019.2019
=1.1/1.1
=1/1
1/1=444444/444444
vì 888887>4444444=>888887/444444>4444444/444444
\(A=\frac{2016}{2017}+\frac{2017}{2018}+\frac{2018}{2019}\)
\(\Rightarrow A=(1-\frac{1}{2017})+(1-\frac{1}{2018})+(1-\frac{1}{2019})\)
\(\Rightarrow A=3-\left(\frac{1}{2017}+\frac{1}{2018}+\frac{1}{2019}\right)\)
\(\left(\frac{1}{2017}+\frac{1}{2018}+\frac{1}{2019}\right)\)<\(\frac{3}{2017}\)<\(1\)
\(\Rightarrow A\)>\(3-1=2\)
\(B=\frac{2016+2017+2018}{2017+2018+2019}\)
\(\Rightarrow B=1-\frac{3}{6054}\)
\(\Rightarrow B=1-\frac{1}{2018}\)
\(B\)<\(1\);\(A\)>\(2\)
\(\Rightarrow A\)>\(B\)
\(\frac{19}{37}+\left(1-\frac{19}{37}\right)\)
\(=\frac{19}{37}+1-\frac{19}{37}\)
\(=\left(\frac{19}{37}-\frac{19}{37}\right)+1\)
\(=0+1=1\)
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Câu hỏi của Nguyễn Thị Yến Nhi - Toán lớp 6 | Học trực tuyến
Có: \(A=\frac{2018^{2019}+1}{2018^{2019}-2017}=\frac{2018^{2019}+1-2018+2018}{2018^{2019}-2017}=\frac{2018^{2019}-2017+2018}{2018^{2019}-2017}=1+\frac{2018}{2018^{2019}-2017}\)
\(B=\frac{2018^{2019}+2}{2018^{2019}-2016}=\frac{2018^{2019}+2-2018+2018}{2018^{2019}-2016}=\frac{2018^{2019}-2016+2018}{2018^{2019}-2016}=1+\frac{2018}{2018^{2019}-2016}\)
Mà: \(\frac{2018}{2018^{2019}-2017}>\frac{2018}{2018^{2019}-2016}\)
\(\Rightarrow1+\frac{2018}{2018^{2019}-2017}>1+\frac{2018}{2018^{2019}-2016}\\ \Rightarrow A>B\)
\(\frac{a^4}{2018}+\frac{b^4}{2019}=\frac{1}{4037}\)
\(\Leftrightarrow\frac{2019a^4+2018b^4}{2018\cdot2019}=\frac{a^2+b^2}{2018+2019}\)
\(\Leftrightarrow\left(2018+2019\right)\left(2019a^4+2018b^4\right)=2018\cdot2019\left(a^2+b^2\right)\)
\(\Leftrightarrow2019^2\cdot a^4+2018^2\cdot b^4+2018\cdot2019\cdot a^4+2018\cdot2019b^4=2018\cdot2019\cdot a^2+2018\cdot2019\cdot b^2\)
\(\Leftrightarrow2019^2\cdot a^4+2018^2\cdot b^4=2018\cdot2019\cdot a^2\left(1-a^2\right)+2018\cdot2019\cdot b^2\left(1-b^2\right)\)
\(\Leftrightarrow\left(2019a^2\right)^2+\left(2018b^2\right)^2=2\cdot2018\cdot2019\cdot a^2\cdot b^2\)
\(\Leftrightarrow\left(2019a^2-2018b^2\right)=0\)
\(\Leftrightarrow2019a^2=2018b^2\Leftrightarrow\frac{a^2}{2018}=\frac{b^2}{2019}=\frac{a^2+b^2}{2018+2019}=\frac{1}{4037}\)
\(\Rightarrow\frac{a^{2018}}{2018^{10009}}=\frac{b^{2018}}{2019^{1009}}=\frac{1}{4037^{1009}}\)
\(\Rightarrow P=\frac{2}{4037^{1009}}\)
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so sánh