Question

Scrieti ca suma de doua patrate perfecte numerele:
13⁷
65
65¹³
29³¹
45²¹
45⁴⁵
29¹¹
25¹⁰¹​

Answer 1

Răspuns:

Salut !

Am sa iti fac 2-3 exercitii pentru a intelege metoda de rezolvare.

13⁷ =

= 13⁶ₓ13

= (13³)²ₓ(9 + 4)

= (13³)²(3² + 2²)

= (13³)²ₓ3² + (13³)²ₓ2²

= (13³ₓ3)² + (13³ₓ2)²

65¹³ =

= 65¹²ₓ65

= (65⁶)²ₓ(64 + 1)

= (65⁶)²ₓ(8² + 1²)

= (65⁶)²ₓ8² + (65⁶)²ₓ1²

= (65⁶ₓ8)² + (65⁶)²

29³¹ =

= 29³⁰ₓ29

= (29¹⁵)²ₓ(25 + 4)

= (29¹⁵)²ₓ(5² + 2²)

= (29¹⁵)²ₓ5² + (29¹⁵)²ₓ2²

= (29¹⁵ₓ5)² + (29¹⁵ₓ2)²

Bafta !