Question

a) Tìm các số tự nhiên x biết: \(8.6+288:\left(x-3\right)^2=50\)

b) Tìm các chữ số x;y để \(A=\overline{x183y}\)chia cho 2;5 và 9 đều dư 1

c) chứng tỏ rằng nếu p là số nguyên tố lớn hơn 3 thì p²-1 chia hết cho 3

Answer 1

 Do A = x183y   chia cho 2 và 5 đều dư 1 nên y = 1. Ta có A = x183y 

Vì A = x183y  chia cho 9 dư 1

→ x183y  - 1 chia hết cho 9

→ x183y chia hết cho 9

↔ x + 1 + 8 + 3 + 0 chia hết cho 9 ↔ x + 3 chia hết cho 9, mà x là chữ số nên x = 6

Vậy x = 6; y = 1

Answer 2

a)

= 48 + 288 : ( x - 3 )² = 50 

288 : ( x - 3 )² = 50 - 48

288: ( x - 3 )²= 2

(x - 3 )²= 288 : 2

(x - 3)²= 144

(x - 3)² = 12²

x - 3 = 12 

x = 12 + 3 = 15

 

Answer 3

p là số ngyên tố lớn hơn 3=>p không chia hết cho 3

=>p²=3k+1

=>p²-1=3k+1-1=3k chia hết cho 3

=>đpcm

 

Answer 4

\(x=6,y=1\)

Answer 5

x=6

y=1

hok tot

Answer 6

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..................................................................................................................................................................................................................................................................................................................................................................................................................................................ko biet