a) 2022 . 999 + 2022

= 2022 . 1000

= 2022000

b) 5 . 2² - 18 : 3

= 5 . 4 - 6

= 20 - 6

= 14

20,22 x 97 + 20,22 : 0,25 - 20,22

= 20,22 x 97 + 20,22 x 4 - 20,22

= 20,22 x ( 97 + 4 - 1 )

= 20,22 x 100

= 2022

x . ( x³ )² = x⁵

x . x⁶ = x⁵

x⁷ = x⁵

=> x \(\in\) { 0; \(\pm\)1 }

2 . [ ( -3 ) + 1 ] + 10 

= 2. ( -2 ) + 10

= -4 + 10

= 10 - 4

= 6

a) 15 -(-203 ) - 203

= 15 + 203 - 203

= 15 + ( 203 - 203 )

= 15 + 0

= 15

10000

A = \(\dfrac{4}{5.9}+\dfrac{4}{9.13}+...+\dfrac{4}{403.407}\)

A = 4( \(\dfrac{1}{5.9}+\dfrac{1}{9.13}+...+\dfrac{1}{403.407}\) )

A = 4 ( \(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-...-\dfrac{1}{407}\) )

A = 4 . ( \(\dfrac{1}{5}-\dfrac{1}{407}\) )

A = 4 . \(\dfrac{402}{2035}\)

A = \(\dfrac{1608}{2035}\)

tự so sánh đi

xy - x + y = 6

x( y - 1 ) + ( y - 1 ) = 5

( y - 1 ) . ( x + 1 )

Ư( 5 ) = { \(\pm1;\pm5\) }

=> ta có bảng sau:

=> x \(\in\) { -2; -6; 0; 4 }

y \(\in\) { 0; -4; 2; 6 }

b) ( 4x + 3 ) \(⋮\) ( x - 2 ) 

4x + 3 = 4x - 2 + 5

4x - 2 \(⋮\) x - 2

=> 5 \(⋮\) x - 2

x - 2 \(\in\) Ư(5)

Ư( 5 ) = { \(\pm1;\pm5\) }

=> ta có bảng sau:

vậy x \(\in\) { 1; \(\pm3\); 7 }

a) A = 2 + 2² + 2³ + ... + 2¹⁰

2A = 2² + 2⁴ + 2⁵ + ... + 2¹¹

2A = ( 2² + 2⁴ + 2⁵ + ... + 2¹¹ ) - ( 2 + 2² + 2³ + ... + 2¹⁰ )

A = 2¹¹ - 2

A + 2 = 2^{x - 1} \(\rightarrow\)  2¹¹ - 2 + 2 = 2^{x -1}

2¹¹ = 2^{x - 1}

<=> 11 = x - 1

x = 11 + 1

x = 12