x : 2 = x : 3
so sánh A va B
A = 1998 x 1998
B = 1996 x 2000
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(X -10/1994 -1) + (X-8/1996 - 1) + (X-6/1998 - 1)+ (X-4/2000 - 1) + (X-2/2002 - 1) = (X-2002/2 - 1) + (X-2000/4 - 1) + (X-1998/6 - 1) + (X-1996/8 - 1) + (X-1994/10 - 1)
=> x-2004/1994 + x-2004/1996 + x-2004/1998 + x-2004/2000 + x-2004/2002 = x-2004/2 + x-2004/4 + x-2004/6 + x-2004/8 + x-2004/1994
=> x-2004/1994 + x-2004/1996 + x-2004/1998 + x-2004/2000 + x-2004/2002 - x-2004/2 - x-2004/4 - x-2004/6 - x-2004/8 - x-2004/1994 = 0
=> (x - 2004)(1/994 + 1/1996 + 1/1998 + 1/2000 + 1/2002 + 1/2 + 1/4 + 1/6 + 1/8) = 0
Mà (1/994 + 1/1996 + 1/1998 + 1/2000 + 1/2002 + 1/2 + 1/4 + 1/6 + 1/8) \(\ne\)0
=> x - 2004 = 0
=> x = 2004
Vậy x = 2004
\(B=1996.2000=\left(1998-2\right)\left(1998+2\right)=1998^2+2.1998-2.1998-2^2=1998^2-4< 1998^2=1998.1998=A\)
\(B=1996\cdot2000\)
\(=\left(1998-2\right)\left(1998+2\right)\)
\(=1998^2-4< 1998^2\)
hay A>B
Vậy: A lớn hơn B 4 đơn vị
1 a, \(A=1998.1998=1998^2\)
\(B=1996.2000=\left(1998-2\right).\left(1998+2\right)=1998^2-4\)
Vì \(1998^2>1998^2-4\)
\(\Rightarrow A=1998.1998>B=1996.2000\)
Vậy A>B
b, \(A=2000.2000=2000^2\)
\(B=1990.2010=\left(2000-10\right).\left(2000+10\right)=2000^2-10\)
Vì \(2000^2>2000^2-10\)
\(\Rightarrow A=2000.2000>B=1990.2010\)
Vậy A>B
1) 2x x 4 = 126
=> 2x = 126 : 4
=> 2x = 32 = 25 => x = 5
Vậy x = 5
2) a, Ta có:
1998 × 1998 = (1996 + 2) × 1998 = 1996 × 1998 + 2 × 1998
1996 × 2000 = 1996 × (1998 + 2) = 1996 × 1998 + 1996 × 2
Vì 2 × 1998 > 1996 x 2 => 1998 × 1998 > 1996 × 2000
b, Ta có:
2000 × 2000 = (1990 + 10) × 2000 = 1990 × 2000 + 10 × 2000
1990 × 2010 = 1990 × (2000 + 10) = 1990 × 2000 + 1990 × 10
Vì 10 × 2000 > 1990 × 10 => 2000 × 2000 > 1990 × 2010
\(\left(\frac{x-10}{1994}-1\right)\)+\(\left(\frac{x-8}{1996}-1\right)\)+\(\left(\frac{x-6}{1998}-1\right)\)+\(\left(\frac{x-4}{2000}-1\right)\)+\(\left(\frac{x-2}{2002}-1\right)\)=\(\left(\frac{x-2002}{2}-1\right)\)+\(\left(\frac{x-2000}{4}-1\right)\)+\(\left(\frac{x-1998}{6}-1\right)\)+\(\left(\frac{x-1996}{8}-1\right)\)+\(\left(\frac{x-1994}{10}-1\right)\)
suy ra \(\frac{x-2004}{1994}\)+\(\frac{x-2004}{1996}\)+\(\frac{x-2004}{1998}\)+\(\frac{x-2004}{2000}\)+\(\frac{x-2004}{2002}\)=\(\frac{x-2004}{2}\)+\(\frac{x-2004}{4}\)+\(\frac{x-2004}{6}\)+\(\frac{x-2004}{8}\)+\(\frac{x-2004}{10}\)
suy ra \(\frac{x-2004}{1994}\)+\(\frac{x-2004}{1996}\)+\(\frac{x-2004}{1998}\)+\(\frac{x-2004}{2000}\)+\(\frac{x-2004}{2002}\)- \(\frac{x-2004}{2}\)- \(\frac{x-2004}{4}\)- \(\frac{x-2004}{6}\)- \(\frac{x-2004}{8}\)- \(\frac{x-2004}{10}\)=0
suy ra (x-2004) . ( \(\frac{1}{1994}\)+\(\frac{1}{1996}\)+\(\frac{1}{1998}\)+\(\frac{1}{2000}\)+\(\frac{1}{2002}\)-\(\frac{1}{2}\)-\(\frac{1}{4}\)-\(\frac{1}{6}\)- \(\frac{1}{8}\)- \(\frac{1}{10}\))=0
Vì \(\frac{1}{1994}\)+\(\frac{1}{1996}\)+\(\frac{1}{1998}\)+\(\frac{1}{2000}\)+\(\frac{1}{2002}\)-\(\frac{1}{2}\)-\(\frac{1}{4}\)-\(\frac{1}{6}\)- \(\frac{1}{8}\)- \(\frac{1}{10}\) khác 0
nên x-2004=0 suy ra x=2004
2009 . 2001 < 2010 .2010 2010 .2007 > 2005. 2009 2011.1998 > 1996.2000 2012. 2000> 2010. 1990 dấu chấm là dấu nhân cho mik k đi ban mik cm
a) A = 199 x 201
= 199 x 200 + 199
B = 200 x 200
= 200 x 199 + 200
A = 199 x 200 +199 va B = 199 x 200 + 200
=> A < B
b) Có 35 x 53 < 53 x 54 ; -18 < 35
=> C < D
c) E = 1998 x 1998
E = 1998 x 2000 - 1998 x 2
F = 1996 x 2000
F = 1998 x 2000 - 2 x 2000
ma 1998 x 2 < 2 x 2000
=> 1998 x2000 - 1998 x 2 > 1998 x 2000 - 2 x 2000
=> E < F
a > A < B
b> C < D
c> E > F
k mk nha học tốt
Ta có:
\(A=1998\times1998=1998^2\)
\(B=1996\times2000=\left(1998-2\right)\left(1998+2\right)\)
\(=1998^2-2^2=1998^2-4\)
Vì \(1998^2>1998^2-4\Rightarrow A>B\)
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