Question

So sánh \(C=\frac{2011^{2012}+1}{2011^{2013}+1}\)và \(D=\frac{2011^{2013}+1}{2011^{2014}+1}\)

Answer 1

D=\(\frac{2011^{2013}+1}{2011^{2014}+1}\)

 <\(\frac{2011^{2013}+1+2010}{2011^{2014}+1+2010}\)

 <\(\frac{2011^{2013}+2011}{2011^{2014}+2011}\)

<\(\frac{2011\left(2011^{2012}+1\right)}{2011\left(2011^{2013}+1\right)}\)

 <\(\frac{2011^{2012}+1}{2011^{2013}+1}\)

<C

Vậy C>D

Answer 2

C>D nhé

Answer 3

Cách 2:

Ta có: \(2011C=\frac{2011^{2013}+2011}{2011^{2013}+1}=1+\frac{2010}{2011^{2013}+1}\)

\(2011D=\frac{2011^{2014}+2011}{2011^{2014}+1}=1+\frac{2010}{2011^{2014}+1}\)

Mà \(\frac{2010}{2011^{2013}+1}>\frac{2010}{2011^{2014}+1}\Rightarrow1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\)

\(\Rightarrow2011C>2011D\)

\(\Rightarrow C>D\)

Vậy C > D

Answer 4

C>D nhé bạn

Answer 5

C > D nha

Answer 6

C > D nha!

Answer 7

C > D nhg bạn Công chúa ... bảo \(\frac{2011\left(2011^{2012}+1\right)}{2011\left(2011^{2013}+1\right)}< \frac{2011^{2012}+1}{2011^{2013}+1}\)là sai vì cả tử và mẫu rút gọn đi 2011 thì phải như thế này :\(\frac{2011\left(2011^{2012}+1\right)}{2011\left(2011^{2013}+1\right)}=\frac{2011^{2012}+1}{2011^{2013}+1}\)

Answer 8

\(\widehat{xOz}=120^o;\widehat{xOy}=60^o;\widehat{xOy},\widehat{yOz}\)là hai góc kề nhau. Cm: Tia Oy là tia phân giác của \(\widehat{xOz}\) .. Tính flames it

Answer 9

nhan C va D voi 2011 roi tach ra thanh tong voi 1

Answer 10

\(D\)=\(\frac{2011^{2013}+1}{2011^{2014}+1}< \frac{2011^{2013}+1+2010}{2011^{2014}+1+2010}=\frac{2011^{2013}+2011}{2011^{2014}+2011}\)

\(=\frac{2011^{2012}+1}{2011^{2013}+1}\)=\(C\)\(\Rightarrow C>D\)

Answer 11

Ta có: 2011²⁰¹³ < 2011²⁰¹⁴ nên 2011²⁰¹³ + 1 < 2011²⁰¹⁴ +1

\(\Rightarrow\frac{2011^{2013}+1}{2011^{2014}+1}< 1\)

\(\Rightarrow\frac{2011^{2013}+1}{2011^{2014}+1}< \frac{2011^{2013}+1+2010}{2011^{2014}+1+2010}=\frac{2011^{2013}+2011}{2011^{2014}+2011}\)

                                 \(=\frac{2011\cdot\left(2011^{2012}+1\right)}{2011\cdot\left(2011^{2013}+1\right)}=\frac{2011^{2012}+1}{2011^{2013}+1}\)     

\(\Rightarrow\frac{2011^{2013}+1}{2011^{2014}+1}< \frac{2011^{2012}+1}{2011^{2012\cdot3}+1}\)hay D < C

                                                         Vây D < C

Answer 12

D=\(\frac{2011^{2013}+1}{2011^{2014^{ }}+1}\)

\(\Rightarrow\)\(\frac{2011^{2013}+1+2010}{2011^{2014}+1+2010}\)

\(\Rightarrow\)\(\frac{2011^{2013}+2011}{2011^{2014}+2011}\)

\(\Rightarrow\)\(\frac{2011\left(2011^{2012}+1\right)}{2011\left(2011^{2013}+1\right)}\)

\(\Rightarrow\)\(\frac{2011^{2012}+1}{2011^{2013}+1}\)

\(\Rightarrow\)C > D

Answer 13

c>d ok

Answer 14

Ủa, bài làm của công chúa họ lê sai mà vẫn được chọn là sao?

Answer 15

So sánh \(C=\frac{2011^{2012}+1}{2011^{2013}+1}\) và \(D=\frac{2011^{2013}+1}{2011^{2014}+1}\)

+) \(2011.C=\frac{2011\left(2011^{2012}+1\right)}{2011^{2013}+1}\)

                      \(=\frac{2011^{2013}+2011}{2011^{2013}+1}\)

                        \(=\frac{2011^{2013}+1+2010}{2011^{2013}+1}\)

                        \(=\frac{2011^{2013}+1}{2011^{2013}+1}+\frac{2010}{2011^{2013}+1}\)

                        \(=1+\frac{2010}{2011^{2013}+1}\)

+) \(2011.D=\frac{2011\left(2011^{2013}+1\right)}{2011^{2014}+1}\)

                      \(=\frac{2011^{2014}+2011}{2011^{2014}+1}\)

                        \(=\frac{2011^{2014}+1+2010}{2011^{2014}+1}\)

                        \(=\frac{2011^{2014}+1}{2011^{2014}+1}+\frac{2010}{2011^{2014}+1}\)

                        \(=1+\frac{2010}{2011^{2014}+1}\)

+) Vì \(\frac{2010}{2011^{2013}+1}>\frac{2010}{2011^{2014}+1}\) 

\(\Rightarrow1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\)

Hay \(C>D\)

  

Answer 16

Ta có : \(2011C=\frac{2011^{2013}+2011}{2011^{2013}+1}=1+\frac{2010}{2011^{2013}+1}\)(1)

\(2011D=\frac{2011^{2014}+2011}{2011^{2014}+1}=1+\frac{2010}{2011^{2014}+1}\)(2)

Từ 1 và 2 \(=>1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\)

\(=>2011C>2011D\)

\(=>C>D\)

Answer 17

C>D 

:c

:d

XD

Xd

X)\

Answer 18

C= (2011²⁰¹²+1)(2011²⁰¹⁴+1) / (2011²⁰¹³+1)(2011²⁰¹⁴+1)

D=(2011²⁰¹³+1)(2011²⁰¹³+1) / (2011²⁰¹⁴+1)(2011²⁰¹³+1)

Bây giờ C và D có mẫu số chung nên ta đi so sánh tử số

C=2011²⁰¹²(2011²⁰¹⁴+1)+1(2011²⁰¹⁴+1)

D=2011²⁰¹³(2011²⁰¹³+1)+1(2011²⁰¹³+1)

C=2011⁴⁰²⁶+2011²⁰¹²+2011²⁰¹⁴+1

D=2011⁴⁰²⁶+2011²⁰¹³+2011²⁰¹³+1

C=2011²⁰¹²+2011²⁰¹⁴

D=2011²⁰¹³+2011²⁰¹³

C=2011²⁰¹²(1+2011²)

D=2011²⁰¹²(2011+2011)

Vậy nên C>D