Bài 1: tính nhanh
a)997.1003
b)1004^2
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\(A=\left(6-\dfrac{2}{3}+\dfrac{1}{2}\right)-\left(5+\dfrac{5}{3}-\dfrac{3}{2}\right)-\left(3-\dfrac{7}{3}+\dfrac{5}{2}\right)\\ A=\dfrac{35}{6}-\dfrac{31}{6}-\dfrac{19}{6}=-\dfrac{15}{6}\)
a) \(29.31=\left(30-1\right)\left(30+1\right)=30^2-1=900-1=899\)
b) \(33,3^2-2.33,3.3,3+3,3^2=\left(33,3-3,3\right)^2=30^2=900\)
c) \(20,1.19,9=\left(20+0,1\right)\left(20-0,1\right)=20^2-0,1^2=400-0.01=399,99\)
d) \(37^2+2.37.13+13^2=\left(37+13\right)^2=50^2=2500\)
1
a)48,124
b)-28,538
c)56,96
d)111,5
Câu 2
a)132,1
b)21,35
Câu 3
a)4,8
b)71,5
Lời giải:
$A=(99-97)+(95-93)+(91-89)+...+(7-5)+(8-1)$
$=\underbrace{2+2+2+...+2}_{24}+7$
$=2\times 24+7$
$=55$
Ta có: 99–97 +95–93+...+7–5+3−1
=(99−97)+(95−93)+...+(7−5)+(3−1)
=2+2+...+2+2 (có 25 số 2)
=2.25
=50
\(=\left(300-52\right)\left(300+52\right)=300^2-52^2\\ =90000-2704=87296\)
a)\(37.x6.5-7.5x3.4-6.6x7.5+3.5x37.5\)
=\(7.5x5x6.5-7.5x3.4-6.6x7.5+3.5x7.5x5\)
=\(7.5x\left(5x6.5-3.4-6.6+3.5x5\right)\)
=\(7.5x\left(2x6.5-10\right)\)
=\(7.5x\left(13-10\right)\)
=\(7.5x3\)
=\(22.5\)
\(a,=15\left(\dfrac{2121}{4343}+\dfrac{222222}{434343}\right)=15\left(\dfrac{21}{43}+\dfrac{22}{43}\right)=15\cdot1=15\)
a, 1004 .2009 + 1005 = (1005-1) .2009 +1005
= 1005 .2009 -2009 +1005
= 1005 .2009 -1004
Vậy ( 1004 .2009 +1005) / (1005 .2009 -1004) =1
b, 1004 .2010 +1 = 1004 .2009 +1004 +1
= (1006 -2) .2009 +1005
= 1006 .2009 -2 .2009 +1005
= 1006 .2009 -4008 +1005
= 1006 .2009 -3013
Vậy (1004 .2010 +1) / (1006 .2009 -3013) = 1
c, 2007 .2009 -2 = 2007.(2008+1) -2
= 2007.2008 +2007 -2
= 2007.2008 +2005
= (2008-1) .2008 +2005
= 2008 .2008 -2008 +2005
= 2008 .2008 -3
Vậy (2008 .2008 -3) / (2007 .2009 -2) =1
a997*1003=(1000-3)*(1000+3)=1000^3+3^3=1000000000-27=999999973
b10004^2=(1000+4)^2=1000^2+2*4*1000+4^2=1008016