1014 x 70 :100
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1014 : ( 124 - x ) = 13
124 - x = 1014 : 13
124 - x = 78
x = 124 - 78
x = 46
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\(\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...\left(1-\frac{1015}{1014}\right)\)
\(=\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...\left(1-\frac{1014}{1014}\right).\left(1-\frac{1015}{1014}\right)\)
\(=\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...\left(1-1\right).\left(1-\frac{1015}{1014}\right)\)
\(=\left(1-\frac{1}{1014}\right).\left(1-\frac{2}{1014}\right).\left(1-\frac{3}{1014}\right).\left(1-\frac{4}{1014}\right)...0.\left(1-\frac{1015}{1014}\right)\)
\(=0\)
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A=|x-1006|-|x+1014|
Áp dụng bđt: |a|-|b|<|a-b| ta có:
|a|-|b|<|a-b|
<=>(|a|-|b|)2< (|a-b|)2
<=>a2-2|ab|+b2< a2-2ab+b2
<=>-|ab| < -ab <=> |ab| > ab (luôn đúng)
Dấu "=" xảy ra khi và chỉ khi: ab>0
Áp dụng bđt vào biểu thức: A=|x-1006|-|x+1014|
Ta có:A=|x-1006|-|x+1014| < |x-1006-x-1004|=2010
Vậy Amax=2010 khi x> 1006 ; x< -1014
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2017.2015-2014.1014-4031
=4064255-2042196-4031
=2022059-4031
=2018028
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`A=(10^14-1)/(10^15-11)`
`=>10A=(10^15-10)/(10^15-11)`
`=>10A=(10^15-11+1)/(10^15-11)`
`=>10A=1+1/(10^15-1)`
`=>A>1/10`
`B=(10^14+1)/(10^15+9)`
`=>10B=(10^15+10)/(10^15+9)`
`=>10A=(10^15+9+1)/(10^15+9)`
`=>10A=1+1/(10^15+9)`
Vì `1/(10^15-1)>1/(10^15+9)`
`=>10B>10A`
`=>B>A`
Giải:
\(A=\dfrac{10^{14}-1}{10^{15}-11}\)
\(10A=\dfrac{10^{15}-10}{10^{15}-11}\)
\(10A=\dfrac{10^{15}-11+1}{10^{15}-11}\)
\(10A=1+\dfrac{1}{10^{15}-11}\)
Tương tự:
\(B=\dfrac{10^{14}+1}{10^{15}+9}\)
\(10B=\dfrac{10^{15}+10}{10^{15}+9}\)
\(10B=\dfrac{10^{15}+9+1}{10^{15}+9}\)
\(10B=1+\dfrac{1}{10^{15}+9}\)
Vì \(\dfrac{1}{10^{15}-11}>\dfrac{1}{10^{15}+9}\) nên \(10A>10B\)
\(\Rightarrow A>B\)
Chúc bạn học tốt!
1014 x 70 : 100 = 709,8
HT