Đề bài là gì bạn?

   A = 1 + 2¹ + 2² + 2³ + ... + 2²⁰²³

2.A = 2 + 2² + 2³ + 2⁴ + ... + 2²⁰²⁴

2A - A = 2 + 2² + 2³ + 2²⁰²³ - (1 + 2 + 2² + 2³ + 2⁴ + ... + 2²⁰²³)

A        =   2 + 2² + 2³ + 2²⁰²³ + 2²⁰²⁴- 1 - 2 - 2² - 2³ - 2⁴ - ... - 2²⁰²³

A        =    (2 - 2) + (2² - 2²) + (2³ - 2³) + (2⁴ - 2⁴) + ...+(2²⁰²⁴ - 1)

A        =      0   + 0  +  0 + 0 + .... + 2²⁰²⁴ - 1

A        = 2²⁰²⁴ - 1

\(2xy-y+2x-7=0\)

\(\Leftrightarrow2xy+2x-y-1=6\)

\(\Leftrightarrow2x\left(y+1\right)-\left(y+1\right)=6\)

\(\Leftrightarrow\left(2x-1\right)\left(y+1\right)=6\)

Do \(2x-1\) luôn lẻ với mọi x nguyên nên ta chỉ cần xét các trường hợp \(2x-1\) là ước lẻ của 6

Ta có bảng giá trị sau:

Vậy \(\left(x;y\right)=\left(-1;-3\right);\left(0;-7\right);\left(1;5\right);\left(2;1\right)\)

a) \(5+3^{x+1}=86\)

\(=>3^{x+1}=86-5\)

\(=>3^{x+1}=81=3^4\)

\(=>x+1=4\) ( cùng cơ số )

\(=>x=4-1\)

\(=>x=3\)

b) \(15:\left(x+2\right)=\left(3^3+3\right):10\)

\(=>15:\left(x+2\right)=\left(27+3\right):10\)

\(=>15:\left(x+2\right)=30:10=3\)

\(=>x+2=15:3\)

\(=>x+2=5\)

\(=>x=5-2\)

\(=>x=3\)

c) \(\left(9x+2\right).4=80\)

\(=>9x+2=80:4\)

\(=>9x+2=20\)

\(=>9x=20-2\)

\(=>9x=18\)

\(=>x=18:9\)

\(=>x=2\)

d) \(\left(245-x\right)+7^2=14\)

\(=>\left(245-x\right)+14=14\)

\(=>245-x=14-14\)

\(=>245-x=0\)

\(=>x=245-0\)

\(=>x=245\)

?

nguyên dương hả bạn

a, \(\left(-2\right)x-\left(-21\right)=15\)

\(=>\left(-2\right)x+21=15\)

\(=>\left(-2\right)x=15-21\)

\(=>\left(-2\right)x=-6\)

\(=>x=\left(-6\right):\left(-2\right)\)

\(=>x=3\)

________

b, \(\left(3x-2^2\right).7^3=7^4\)

\(=>3x-4=7^4:7^3\)

\(=>3x-4=7\)

\(=>3x=7+4\)

\(=>3x=11\)

\(=>x=\dfrac{11}{3}\)

(-2).x+21=15

(-2).x=15-21

(-2).x=6

x=6:(-2)

x=3

-23+150+(-9)+1913

=127+(-9)+1913

=118+1913

=2031

-23 + 150 + (-9) + 1913

= 127 + (-9) + 1913

= 118 + 1913

= 2031

a.

\(4x-3⋮x-2\Rightarrow4x-8+5⋮x-2\)

\(\Rightarrow4\left(x-2\right)+5⋮x-2\)

Do \(4\left(x-2\right)⋮x-2\Rightarrow5⋮x-2\Rightarrow x-2=Ư\left(5\right)\)

\(\Rightarrow x-2=\left\{-5;-1;1;5\right\}\)

\(\Rightarrow x=\left\{-3;1;3;7\right\}\)

b.

\(xy-2x+2y=5\)

\(\Leftrightarrow xy-2x+2y-4=5-4\)

\(\Leftrightarrow x\left(y-2\right)+2\left(y-2\right)=1\)

\(\Leftrightarrow\left(x+2\right)\left(y-2\right)=1\)

Ta có bảng giá trị:

Vậy \(\left(x;y\right)=\left(-3;1\right);\left(-1;3\right)\)