Toán Lớp 7: Cho A=2021^2020+2018/2021^2021+2018 và B=2021^2019+1/2021^2020+1 so sánh A và B

Question

Toán Lớp 7:  Cho A=2021^2020+2018/2021^2021+2018 và B=2021^2019+1/2021^2020+1 so sánh A và B

ngocle44 · Answer

Giải đáp:   $A<B$   Lời giải và giải thích chi tiết:   $A= dfrac{2021^{2020}+2018}{2021^{2021}+2018}   Rightarrow2021A= dfrac{2021.(2021^{2020}+2018)}{2021^{2021}+2018}   Rightarrow2021A= dfrac{2021^{2021}+2018.2021}{2021^{2021}+2018}   Rightarrow2021A= dfrac{2021^{2021}+2018+2018.2020}{2021^{2021}+2018}   Rightarrow2021A= dfrac{2021^{2021}+2018}{2021^{2021}+2018}+ dfrac{2018.2020}{2021^{2021}+2018}   Rightarrow2021A=1+ dfrac{2018.2020}{2021^{2021}+2018}  B= dfrac{2021^{2019}+1}{2021^{2020}+1}   Rightarrow2021B= dfrac{2021.(2021^{2019}+1)}{2021^{2020}+1}   Rightarrow2021B= dfrac{2021^{2020}+2021}{2021^{2020}+1}   Rightarrow2021B= dfrac{2021^{2020}+1+2020}{2021^{2020}+1}   Rightarrow2021B= dfrac{2021^{2020}+1}{2021^{2020}+1}+ dfrac{2020}{2021^{2020}+1}   Rightarrow2021A=1+ dfrac{2020}{2021^{2020}+1}   Rightarrow dfrac{2020}{2021^{2020}+1}= dfrac{2018.2020}{2018.2021^{2020}+2018}   Rightarrow dfrac{2018.2020}{2018.2021^{2020}+2018}> dfrac{2018.2020}{2021^{2021}+1}   Rightarrow 2021A<2021B   Rightarrow A<B$

kimoanh34 · Answer

Sau đ&acirc;y l&agrave; b&agrave;i l&agrave;m của m&igrave;nh bạn tham khảo :     Ta biến đổi mũ l&agrave; nh&acirc;n     A=  2021 x 2020+2018 x 2021 x 2021+2018       A=4082420 + 8242401938 + 2018       A=8246486376       B=2021 x 2019+1 : 2021 x 2020 + 1      B=   4100609 + 4082420 + 1     B= 8183030     Ta so s&aacute;nh v&igrave; A c&oacute; nhiều chữ số hơn B n&ecirc;n ta kết luận A > B     Xin hay nhất cho nh&oacute;m ạ     Cam kết kh&ocirc;ng vi phạm luật Hoidap247     #hoahathihoa     @Companion Team