Question

ajutor la ex 23
DAU COROANA REPEDEEE ​

Answer 1

Răspuns:

a) (7³² + 4·7³⁰) : 53 = 7³⁰

b) (5²³ + 5²² + 5²¹) : 31 = 5²¹

c) (3¹⁰⁰ + 3¹⁰¹ + 3¹⁰² + 3¹⁰³) : 40 = 3¹⁰⁰

d) (8⁴¹+8⁴²+8⁴³+8⁴⁴+8⁴⁵+8⁴⁶) : 73 = 8⁴¹·513

Explicație pas cu pas:

Toate împărțirile au restul 0.

a)

7³² + 4·7³⁰ = 7³⁰ (7² + 4) = 7³⁰ (49 + 4) = 7³⁰·53

7³⁰·53 : 53 = 7³⁰

b)

5²³ + 5²² + 5²¹ = 5²¹(5² + 5 + 1) = 5²¹(25+5+1) = 5²¹·31

5²¹·31 : 31 = 5²¹

c)

3¹⁰⁰ + 3¹⁰¹ + 3¹⁰² + 3¹⁰³ = 3¹⁰⁰(1+3+3²+3³) = 3¹⁰⁰(1+3+9+7) = 3¹⁰⁰·40

(3¹⁰⁰·40):40 = 3¹⁰⁰

d)

8⁴¹+8⁴²+8⁴³+8⁴⁴+8⁴⁵+8⁴⁶ = 8⁴¹(1+8+8²+8³+8⁴+8⁵) =

= 8⁴¹(1+8+64+512+4096+32768) = 8⁴¹·37449 = 8⁴¹·513·73

(8⁴¹·513·73) : 73 = 8⁴¹·513