1) so sánh a) A=2^18-3/2^20-3 B=2^20-3/2^22-3 b)A=2013^2010+1/2013^2011+1 B=2013^2011-2/2013^2012-2 04/09/2021 Bởi Serenity 1) so sánh a) A=2^18-3/2^20-3 B=2^20-3/2^22-3 b)A=2013^2010+1/2013^2011+1 B=2013^2011-2/2013^2012-2
$1$. Ta có: $a$) $A = \dfrac{2^{18}-3}{2^{20}-3}$ $2^2A = \dfrac{2^{20} – 4.3}{2^{20}-3}$ $4A = \dfrac{2^{20} – 12}{2^{20}-3}$ $4A = \dfrac{2^{20} – 3 – 9}{2^{20} – 3}$ $4A = 1 – \dfrac{9}{2^{20}-3}$ $B = \dfrac{2^{20}-3}{2^{22}-3}$ $2^2B = \dfrac{2^{22} – 4.3}{2^{22}-3}$ $4B = \dfrac{2^{22} – 12}{2^{22}-3}$ $4B = \dfrac{2^{22} – 3 – 9}{2^{22} – 3}$ $4B = 1 – \dfrac{9}{2^{22}-3}$ Vì $\dfrac{9}{2^{22}-3} < \dfrac{9}{2^{20}-3}$ $⇒$ $B > A$ $b$) $A = \dfrac{2013^{2010} +1}{2013^{2011} +1}$ $2013A = \dfrac{2013^{2011} + 2013}{2013^{2011}+1}$ $2013A = 1 + \dfrac{2013}{2013^{2011} + 1}$ $B = \dfrac{2013^{2011} -2}{2013^{2012} -2}$ $2013B = \dfrac{2013^{2012} – 4026}{2013^{2012}-2}$ $2013B = \dfrac{2013^{2012} – 2 – 4024}{2013^{2012}-2}$ $2013B = 1 – \dfrac{4024}{2013^{2012} -2}$ Vì $1 – \dfrac{4024}{2013^{2012} -2} < 1 + \dfrac{2013}{2013^{2011} + 1}$ $⇒B < A$ Bình luận
$1$. Ta có:
$a$) $A = \dfrac{2^{18}-3}{2^{20}-3}$
$2^2A = \dfrac{2^{20} – 4.3}{2^{20}-3}$
$4A = \dfrac{2^{20} – 12}{2^{20}-3}$
$4A = \dfrac{2^{20} – 3 – 9}{2^{20} – 3}$
$4A = 1 – \dfrac{9}{2^{20}-3}$
$B = \dfrac{2^{20}-3}{2^{22}-3}$
$2^2B = \dfrac{2^{22} – 4.3}{2^{22}-3}$
$4B = \dfrac{2^{22} – 12}{2^{22}-3}$
$4B = \dfrac{2^{22} – 3 – 9}{2^{22} – 3}$
$4B = 1 – \dfrac{9}{2^{22}-3}$
Vì $\dfrac{9}{2^{22}-3} < \dfrac{9}{2^{20}-3}$
$⇒$ $B > A$
$b$) $A = \dfrac{2013^{2010} +1}{2013^{2011} +1}$
$2013A = \dfrac{2013^{2011} + 2013}{2013^{2011}+1}$
$2013A = 1 + \dfrac{2013}{2013^{2011} + 1}$
$B = \dfrac{2013^{2011} -2}{2013^{2012} -2}$
$2013B = \dfrac{2013^{2012} – 4026}{2013^{2012}-2}$
$2013B = \dfrac{2013^{2012} – 2 – 4024}{2013^{2012}-2}$
$2013B = 1 – \dfrac{4024}{2013^{2012} -2}$
Vì $1 – \dfrac{4024}{2013^{2012} -2} < 1 + \dfrac{2013}{2013^{2011} + 1}$
$⇒B < A$
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