-(2012-199+20)-(-199+20)

=-2012+199-20+199-20

=-2012+(200-1)-20+(200-1)-20

=-2012+200+200-1-1-20-20

=-2012+(200+200)-(20+20+1+1)

=-2012+400-42

=-1612-42=-1654

\(\frac{5}{14}\frac{5}{14}\) LÀ NHÂN À

Mình lỡ đánh nhầm 2 lần \(\frac{5}{14}\)nha :)) chỉ 1 lần thôi

\(\frac{x-199}{6}+\frac{x-199}{12}+\frac{x-199}{20}+\frac{x-199}{30}+\frac{x-199}{42}=\frac{5}{14}\)

\(\left(x-199\right)\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)=\frac{5}{14}\)

\(\left(x-199\right)\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)=\frac{5}{14}\)

\(\left(x-199\right)\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}=\frac{5}{14}\right)\)

\(\left(x-199\right)\left(\frac{1}{2}-\frac{1}{7}\right)=\frac{5}{14}\)

\(\left(x-199\right).\frac{5}{14}=\frac{5}{14}\)

\(\Leftrightarrow x-199=1\)

\(\Leftrightarrow x=200\)

a) 126+(−20)+2004+(−106)126+(−20)+2004+(−106)

=2004+126+[(−20)+(−106)]=2004+126+[(−20)+(−106)]

=2004+126+[−(20+106)]=2004+126+[−(20+106)]

=2004+126+(−126)=2004+126+(−126)

=2004+[126+(−126)]=2004+0=2004=2004+[126+(−126)]=2004+0=2004.

b) (−199)+(−200)+(−201)=−(199+200+201)(−199)+(−200)+(−201)=−(199+200+201)

=−(199+201+200)=−[(199+201)+200]=−(199+201+200)=−[(199+201)+200]

=−(400+200)=−600=−(400+200)=−600.

Lời giải:
$199^{20}< 200^{20}=100^{20}.2^{20}=100^{20}.(2^5)^4=100^{20}.32^4$

$< 100^{20}.100^4=100^{24}$

Ta có: 

\(199^{20}< 200^{20}\)\(;\)\(2013^{15}>2000^{15}\)

Lại có: \(200^{20}=\left(200^4\right)^5=\left(16.10^8\right)^5\)

            \(2000^{15}=\left(2000^3\right)^5=\left(8.10^9\right)^5=\left(80.10^8\right)^5\)

Do \(16.10^8< 80.10^8\)

\(\Rightarrow200^{20}< 2000^{15}\)

\(\Rightarrow199^{20}< 2013^{15}\)

Tự làm đê 

ta có :

199²⁰ < 200²⁰

2000¹⁵ < 2003¹⁵

200²⁰ = 200^{4 . 5} = ( 200⁴ ) ⁵

2000¹⁵ = 2000^{3 . 5} = ( 2000³ ) ⁵

giờ ta so sánh 200⁴ và 2000³

200⁴ = 200³ . 200

2000³ = ( 200 . 10 ) ³ = 200³ . 10³ = 200³ . 1000

Vì 200 < 1000 

=> 200⁴ < 2000³ mà 199²⁰ < 200²⁰ < 2000¹⁵ < 2003¹⁵ nên 199²⁰

Ta có: 199²⁰<200²⁰=(8.25)²⁰=(2³.5²)²⁰=2⁶⁰.5⁴⁰

2003¹⁵>2000¹⁵=(16.125)¹⁵=(2⁴.5³)¹⁵=2⁶⁰.5⁴⁵

Vì 2⁶⁰.5⁴⁰<2⁶⁰.5⁴⁵ nên 200²⁰<2000¹⁵

=>199²⁰<2003¹⁵