Question

Problema 37. Vă roooog.
Repeeeedeee. Dau coroană ​

Answer 1

Explicație pas cu pas:

a = 5^(5n+7)

b = 3^(5m+4)

m, n sunt numere naturale

25ab = 25 × 5^(5n+7) × 3^(5m+4) =

= 5^(5n+9) × 3^(5m+4) ==>

==> 25ab are (5n+10)(5m+5) divizori ==>ab are (5n+8)(5m+5) divizori

(5n+10)(5m+5) = 40 + (5n+8)(5m+5)

(5m+5)(5n+10-5n-8) = 40

(5m+5) × 2 = 40

5m + 5 = 20

5m = 15

m = 3 ==> b = 3^19

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9ab = 9×5^(5n+7) × 3^(5m+4) =

= 5^(5n+7) × 3^(5m+6) ==>

==> 9ab are (5n+8)((5m+7) divizori

ab = are (5n+8)(5m+5) divizori

==> (5n+8)(5m+7) = 36+ (5n+8)(5m+5)

(5n+8)(5m+7-5m-5) = 36

(5n+8) × 2 = 36

5n+8 = 18

5n = 18-8=10

n = 2 ==> a = 5^17

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Answer 2

Răspuns:

Explicație pas cu pas: