Tính nhanh
\(\frac{2010\times125+1000}{126\times2010-1010}=\)
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\(\frac{2010.125+1000}{126.2010-1010}=\frac{10\left(201.125+100\right)}{10\left(201.126-101\right)}=\frac{201.125-101+201}{2011.126-101}\)
\(=\frac{201.126-101}{201.126-101}=1\)
=2010 x 125 + 2010x 126 + 1000+1010
=2010 x 125 + 2010 x 126 + 2010
=2010 x ( 125 + 126 +1 )
=2010 x 252
=506520
A = 2006 x 125 + 1000 / 126 x 2005 - 888
A = (2005 + 1) x 125 + 1000 / (125 + 1) x 2005 - 888
A = 2005 x 125 + 125 + 1000 / 125 x 2005 + 2005 - 888
A = 2005 x 125 + 1125 / 125 x 2005 + 1117
A = 1125 / 1117
8 x 2010 x 125 - 2009 x 437 - 2009 x 563
= ( 8 x 125 ) x 2010 - 2009 x ( 437 + 563 )
= 1000 x 2010 - 2009 x 1000
= 1000 x ( 2010 - 2009 )
= 1000 x 1
= 1000
=))
\(\frac{2010\cdot2011+1000}{2012\cdot2010-1010}\)
= \(\frac{2010\cdot2011+1000}{\left(2011+1\right)\cdot2010-1010}\)
= \(\frac{2010\cdot2011+1000}{2011\cdot2010+2010-1010}\)
= \(\frac{2010\cdot2011+1000}{2011\cdot2010+1000}\)
= 1
\(\frac{2010.2011+1000}{2012.2010-1010}\)
\(=\frac{2010.2011+2010-1010}{2012.2010-1010}\)
\(=\frac{2010.\left(2011+1\right)-1010}{2012.2010-1010}\)
\(=\frac{2010.2012-1010}{2012.2010-1010}\)
\(=1\)
Bạn nguyen quang huy sai rồi!!!
Vì 1000/2009>1000/2009+2010 (1)
1010/2010>1010/2009+2010 (2)
Ta cộng theo vế (1) và (2) với nhau nên ta được:
1000/2009+1010/2010>1000/2009+2010 +1010/2009+2010
=>1000/2009+1010/2010>1000+1010/2009+2010
Vậy A<B
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Lời giải:
$(2012\times 2010+2010\times 2008)\times (1+\frac{1}{2}: 1\frac{1}{2}-1\frac{1}{3})$
$=2010\times (2012+2008)\times (1+\frac{1}{2}\times \frac{2}{3}-1\frac{1}{3})$
$=2010\times 4020\times (1+\frac{1}{3}-1\frac{1}{3})$
$=2010\times 4020\times 0=0$
\(A=\frac{2011\times2012}{2011+2012}+\frac{2009\times2010}{2009+2010}\)
\(A=\frac{2011\times2011}{2011+2012}+\frac{2011}{2011+2012}+\frac{2010\times2010}{2009+2010}-\frac{2010}{2009+2010}\)
\(A=\frac{2011\times2011}{2011+2012}+\frac{2010\times2010}{2009+2010}+\frac{2011}{2011+2012}-\frac{2010}{2009+2010}\)
\(A=B+\frac{2011}{2011+2012}-\frac{2010}{2009+2010}\)
\(A=B+\frac{2011}{4023}-\frac{2010}{4019}\)
Dễ thấy \(\frac{2011}{4023}-\frac{2010}{4019}< 0\)
\(\Rightarrow A< B\)
Bổ sung đề: So sánh A và B
Ta có:
A. \(2010^{1000}=\frac{1010^{1010}.2010^{1000}}{2010^{2010}}=\left(\frac{101}{201}\right)^{1010}\)
B. \(2010^{1000}=\frac{2010^{2010}.2010^{1000}}{3010^{3010}}=\left(\frac{201}{301}\right)^{3010}\)
Từ \(\frac{101}{201}>\frac{1}{2}>\frac{40401}{90601}=\left(\frac{201}{301}\right)^2\)và \(\frac{201}{301}< 1\)
có: \(\left(\frac{101}{201}\right)^{1010}>\left(\frac{201}{301}\right)^{2.1010}=\left(\frac{201}{301}\right)^{2020}>\left(\frac{201}{301}\right)^{3010}\)
Suy ra \(A=\left(\frac{101}{201}\right)^{1010}.\frac{1}{2010^{1000}}>\left(\frac{201}{301}\right)^{3010}.\frac{1}{2010^{1000}}\) hay A > B
bằng 1 bạn ạ
bằng 1 bạn ạ