Tìm hai số tự nhiên a;b sao cho (a-2)(2b+3) = 26
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1) 12 = 1.12 = 2.6 = 3.4 = 4.3 = 6.2 = 12.1
2) 12 = 1.12 = 2.6 = 3.4
Vậy (a; b) ∈ {(1; 12); (2; 6); (3; 4)}
3) 30 = 1.30 = 2.15 = 3.10 = 5.6 = 6.5 = 10.3 = 15.2 = 30.1
4) 30 = 30.1 = 15.2 = 10.3 = 6.5
Vậy (a; b) ∈ {(30; ); (15; 2); (10; 3); (6; 5)}
a, Ta có: 12 = 1 x 12; 2 x 6; 3 x 4
b, Ta có: 12 = 1 x 12; 2 x 6; 3x 4
Theo đề bài, ta có điều kiện: a < b
=> a ϵ {1; 2; 3}
=> b ϵ {12; 6; 4}
Vậy các cặp số (a; b) cần tìm là:
(a; b) ϵ {(1; 12); (2; 6); (3; 4)}
c, Ta có: 30 = 1 x 30; 2 x 15; 3 x 10; 5 x 6
d, Ta có: 30 = 1 x 30; 2 x 15; 3 x 10; 5 x 6
Theo đề bài, ta có điều kiện: a > b
=> a = 30; b = 1
=> a = 15; b = 2
=> a = 10; b = 3
=> a = 6; b = 5
Vậy ta có các cặp số (a; b) thỏa mãn đề bài là:
(a; b) ϵ {(30; 1); (15; 2); (10; 3); (6; 5}
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a) goi hai so la a ; b va a >b
vi UCLN(a,b)=18=>a=18k ; b=18q (trong do UCLN (k,q)=1 va k>q)
=>a+b=162
18k+18q =162
18(k+q)=162
k+q=9
ta co bang sau | |||||||||||||||||||||||
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21453
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- Ta có: a ≥ b ( a,b ∈ N )
ƯCLN ( a, b) = 16
⟹ a chia hết cho 16 ⟹ a = 16.m
⟹ b chia hết cho 16 ⟹ b = 16. n
(m, n là thương; m,n ∈ N, m ≥ n)
ƯCLN(m,n) = 1
⟹ a . b = ƯCLN.BCNN
mà a = 16. m
b = 16. n
Thay số: 16 . m . 16 . n = 16 . 240
16. m . 16. n = 3840
256. m. n = 3840
⟹ m. n = 3840 : 256 = 15
Ta có bảng sau :
m | ... | ... | ... |
n | ... | ... | ... |
a | ... | ... | ... |
b | ... | ... | ... |
⟹ Vậy (a,b) ∈ { (... , ...) ; (... , ....)}
Vì ( a - 2 ) ( 2b + 3 ) = 26 nên a - 2 và 2b + 3 là ước của 26 .
Ư ( 26 ) = { 1 ; 2 ; 13 ; 26 }.
Mà 2b + 3 là số lẻ nên 2b + 3 thuộc { 1 ; 13 }.
+) Nếu 2b + 3 = 1 thì b = rỗng ( vì 1 < 3 và b là số tự nhiên )
+) Nếu 2b + 3 = 13 thì b = 5
=> a - 2 = 2
=> a = 4
Vậy hai số tự nhiên a và b là : 4 và 5
V