(2x+1)(y-3)=12

Vì x;y là số tự nhiên => 2x+1;y-3 là số tự nhiên

                                 => 2x+1;y-3 E Ư(12)

Ta có bảng:

Vậy cặp số tự nhiên (x;y) cần tìm là: (0;15) ; (1;7)

(2x + 1)(y - 3) = 12

=> 2x + 1;y - 3 thuộc Ư(12)

vì x là stn => 2x + 1 là stn, ta có bảng

Ta có : \(2^x+2^{x+1}+2^{x+2}+...+2^{x+2015}=2^{2019}-8\)

\(\Leftrightarrow2^x\left(1+2+2^2+...+2^{2015}\right)=2^{2019}-8\) (1)

Đặt : \(A=1+2+2^2+...+2^{2015}\)

\(\Rightarrow2A=2+2^2+2^3+...+2^{2016}\)

\(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2016}\right)-\left(1+2+2^2+...+2^{2015}\right)\)

\(\Rightarrow A=2^{2016}-1\)

Khi đó (1) trở thành :

\(2^x\left(2^{2016}-1\right)=2^{2019}-2^3\)

\(\Leftrightarrow2^x\left(2^{2016}-1\right)=2^3\left(2^{2016}-1\right)\)

\(\Leftrightarrow2^x=2^3\left(2^{2016}-1\ne0\right)\)

\(\Leftrightarrow x=3\)

Vậy : \(x=3\)

vậy x=3 nhé

\(2^x+2^{x+1}+2^{x+2}+...+2^{x+2015}=2^{2019}-8\)

\(\Leftrightarrow2^x\left(1+2+2^2+...+2^{2015}\right)=2^{2019}-2^3\)

\(\Leftrightarrow2^x\left(2^{2016}-1\right)=2^3\left(2^{2016}-1\right)\)

\(\Leftrightarrow2^x=2^3\)

\(\Leftrightarrow x=3\)

Vậy x = 3

2 ^x + 2^x+1+ 2 ^x+2+.......+ 2^x+2015=2²⁰¹⁹-8

=2^x.( 1+2+2²+2³+.....+ 2 ²⁰¹⁵)=2²⁰¹⁹- 2³

đặt A= 1+2+2²+...+2²⁰¹⁵

=>2A=2+2²+2³+..+2²⁰¹⁶

=>2A -A = ( 2+ 2²+2³+......+2²⁰¹⁶)-(1+2+2²+........+2²⁰¹⁵)=A=2²⁰¹⁶-1

\(\Rightarrow\)2^x.(2²⁰¹⁶-1)=2³.(2²⁰¹⁶-1)

=>x=3

0o0_Boss secret_0o0

Nên ghi dấu \(\Leftrightarrow\) để chỉ hai pt tương đương nhé

Theo đầu bài ta có:
\(2^x+2^{x+1}+2^{x+2}+...+2^{x+2015}=2^{2019}-8\)
\(\Rightarrow2\left(2^x+2^{x+1}+2^{x+2}+...+2^{x+2015}\right)-\left(2^x+2^{x+1}+2^{x+2}+...+2^{x+2015}\right)=2^{2019}-8\)
\(\Rightarrow\left(2^{x+1}+2^{x+2}+2^{x+3}+...+2^{x+2016}\right)-\left(2^x+2^{x+1}+2^{x+2}+...+2^{x+2015}\right)=2^{2019}-8\)
\(\Rightarrow2^{x+2016}-2^x=2^{2019}-8\)
\(\Rightarrow2^x\cdot2^{2016}-2^x=2^3\cdot2^{2016}-2^3\)
\(\Rightarrow2^x\left(2^{2016}-1\right)=2^3\left(2^{2016}-1\right)\)
\(\Rightarrow2^x=2^3\)
\(\Rightarrow x=3\)

cảm ơn

2^x.[1+2+2^2+....+2^2015]­=2^2019-8

ta co A=1+2+2^2+....+2^2015

2A=2+2^2+2^3+....+2^2016

2A-A=2^2016-1

thay A vao ta co 

2^ x.[2^2016-1]=2^2016.2^3-2^3

2^x=2^3.[2^2016-1]:[2^2016-1]

2^x=2^3

=>x=3

2^x+2^x+1+2^x+2+2^x+3+....................+2^x+2015=2^2019-8

2^{x.(1+2+3+...............+2015)}=2²⁰¹¹

=>x.(1+2+3+........+2015)=2011

               Có 2015 số hạng

=>x.[(1+2015).2015:2]=2011

=>x.2031120=2011

=>x                     =\(\frac{2011}{2031120}\)

Vậy x=\(\frac{2011}{2031120}\)

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