Bài 1 : Tìm số nguyên x biết :
a) $2^{x}$ `:` $2^{5}$ `= 32 : 8`
b) `23.75 + 25.23 + 100`
Bài 2 : Tìm x ∈ Z biết:
a) `( 2x – 8 ) . 2 =` $2^{5}$
b) `125 – 3 . ( x + 2 ) = 65`
c) `541 + (218 – x ) = 735`
Bài 3 :
a) Chứng minh A = `2` + $2^{2}$ + $2^{3}$ + $2^{4}$ + … + $2^{30}$ chia hết cho `7`
b) Tìm 3 số nguyên a,b ,c thỏa mãn : a + b = -4 ; b + c = -6 ; c + a = 12 – 4 + 22
c) Chứng minh ( ` 1 + 2 +`$2^{2}$ + $2^{3}$ + $2^{4}$ $+$ $2^{5}$ $+$ $2^{6}$ $+$ $2^{7}$ $+$ $2^{8}$ $+$ $2^{9}$ ) chia hết cho 3
Đáp án:
Bài 2:
a) `( 2x – 8 ).2 =` $2^{5}$
`( 2x – 8 ).2 = 32`
`( 2x – 8 ) = 32 : 2`
`( 2x – 8 ) = 16`
` 2x = 16 + 8`
` 2x = 24`
`x = 24 : 2`
`x = 12`
Vậy `x = 12`
b) `125 – 3 . ( x + 2 ) = 65`
`3 . ( x + 2 ) = 125 – 65`
`3 . ( x + 2 ) = 60`
`( x + 2 ) = 60 : 3`
`( x + 2 ) = 20`
`x = 20 – 2`
`x = 12`
Vậy `x = 12`
c) `541 + ( 218 – x ) = 735`
`( 218 – x ) = 735 – 541`
`( 218 – x ) = 194`
`x = 194 + (-218)`
`x = -24`
Vậy `x = 24`
$3.$
`( 1 + 2 + `$2^{2}$`+` $2^{3}$ $+$ $2^{4}$ $+$ $2^{5}$ $+$ $2^{6}$ $+$ $x^{2}$ $2^{7}$ $+$ $2^{8}$ $+$ $2^{9}$ `)`
$=$ `( 1 + 2 )` + ( `$2^{2}$`+` $2^{3}$ ) $+$ ( $2^{4}$ $+$ $2^{5}$ ) $+$ ( $2^{6}$ $+$ $2^{7}$ )
$+$ ( $2^{8}$ $+$ $2^{9}$ )
`=` `( 1 + 2 )` `+` $2^{2}$ $.$ `( 1 + 2 )` $+$ $2^{4}$ $.$ `( 1 + 2 )` `+` $2^{8}$ $.$ `( 1 + 2 )`
`= 3 +` $2^{2}$ $.$ $3$ $+$ $2^{4}$ `. 3`
`= 3 . (` $2^{2}$ `+` $2^{4}$ `+` $2^{6}$ `+` $2^{8}$ `)` $⋮$ $3$
P/s : Đọc chi tiết trước khi báo cáo !