So sánh 2018/2019 và 2019/2020
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bạn nào làm được thì giúp mình với còn bài này thì mình không biết làm. sorry nha
AI NÓI TỚ NÓI SAI, CÓ NÓI VỀ BÀI ĐÂU MÀ SAI ĐIÊN À MẤY BẠN KIA
\(x=\frac{2019^{2020}+1}{2019^{2019}+1}>\frac{2019^{2020}+1+2018}{2019^{2019}+1+2018}=\frac{2019^{2020}+2019}{2019^{2019}+2019}=\frac{2019\left(2019^{2019}+1\right)}{2019\left(2019^{2018}+1\right)}=\frac{2019^{2019}+1}{2019^{2018}+1}\)(1)
\(y=\frac{2019^{2019}+2020}{2019^{2018}+2020}< \frac{2019^{2019}+2020-2019}{2019^{2018}+2020-2019}=\frac{2019^{2019}+1}{2019^{2018}+1}\left(2\right)\)
Từ (1) và (2) \(\Rightarrow x>y\)
Lời giải:
Ta có:
\(A+1=\frac{2019^{2019}+2019^{2020}}{2019^{2019}-1}=\frac{2019^{2019}.2020}{2019^{2019}-1}\)
\(B+1=\frac{2019^{2019}+2019^{2018}}{2019^{2018}-1}=\frac{2019^{2018}.2020}{2019^{2018}-1}\) \(=\frac{2019^{2019}.2020}{2019^{2019}-2019}>\frac{2019^{2019}.2020}{2019^{2019}-1}\)
$\Rightarrow B+1>A+1$
$\Rightarrow B>A$
để bằng 1 thì 2019/2020 phải cộng với 1/2020
để bằng 1 thì 2018/2019 phải cộng với 1/2019
vì 1/2020<1/2019
=> 2019/2020>2018/2019
Ta có: \(\frac{2019}{2020}=1-\frac{1}{2020}\)
\(\frac{2018}{2019}=1-\frac{1}{2019}\)
Vì \(\frac{1}{2019}>\frac{1}{2020}\) nên \(1-\frac{1}{2019}< 1-\frac{1}{2020}\)
hay \(\frac{2018}{2019}< \frac{2019}{2020}\)
Ta có:\(\frac{2018}{2019}\)<1\(\Rightarrow\)\(\frac{2018}{2019}\)>\(\frac{2018}{2019+2020}\)
\(\frac{2019}{2020}\)<1\(\Rightarrow\)\(\frac{2019}{2020}\)>\(\frac{2019}{2019+2020}\)
\(\Rightarrow\)\(\frac{2018}{2019}\)+\(\frac{2019}{2020}\)>\(\frac{2018}{2019+2020}\)+\(\frac{2019}{2019+2020}\)=\(\frac{2018+2019}{2019+2020}\)
\(\Rightarrow\)A>B
Vậy A>B
Ta có :\(A=\frac{2018}{2019}+\frac{2019}{2020}\)
\(B=\frac{2018+2019}{2019+2020}\)
\(B=\frac{2018}{2019+2020}+\frac{2019}{2019+2020}\)
Ta thấy :
\(\frac{2018}{2019}>\frac{2018}{2019+2020}\left(2019< 2019+2020\right)\)
\(\frac{2019}{2020}>\frac{2019}{2019+2020}\left(2020< 2019+2020\right)\)
\(\Rightarrow\frac{2018}{2019}+\frac{2019}{2020}>\frac{2018+2019}{2019+2020}\)
Vậy \(A>B\)
~ Thiên Mã ~
\(1-\frac{2018}{2019}=\frac{1}{2019}.\)
\(1-\frac{2019}{2020}=\frac{1}{2020}.\)
Ta có: 2019<2020 <=> \(\frac{1}{2019}>\frac{1}{2020}.\)
\(\Rightarrow-\frac{1}{2019}< -\frac{1}{2020}.\)
\(\Rightarrow1-\frac{1}{2019}< 1-\frac{1}{2020}.\)
\(\Rightarrow\frac{2018}{2019}< \frac{2019}{2020}.\)
2018/2019 < 2019/2020