Question

Rezolvati-mi si mie urmatoarele exercitii :
Scrieti ca o suma de doua patrate perfecte distincte numerele: a) 9 la puterea 19 b) 65 c) 65 la puterea 13 d) 29 la puterea 31 e) 45 la puterea 21 f) 45 la puterea 45 g) 29 la puterea 11 h)25 la puterea 101.
VA ROGGG E URGENTTT

Answer 1

Suma de 2 patrate perfecte diferite :

a) 9^19 = 9^18 × 9 = (9^9)^2 × (3^2 + 0^2) =

= (9^9 × 3)^2 + (9^9 × 0)^2
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b) 65 = 8^2 + 1^2
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c) 65^13 = 65^12 × 65 = (65^6)^2 × (8^2+1^2) =

= (65^6 × 8)^2 + (65^6 × 1)^2
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d) 29^31 = 29^30 × 29 = (29^15)^2 × (5^2 + 2^2) =

= (29^15 × 5)^2 + (29^15 × 2)^2
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e) 45^21 =45^20 × 45 =(45^10)^2 × (3^2+6^2)=

= (45^10 × 3)^2 + (45^10 × 6)^2
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f) 45^45 = 45^44 × 45 = (45^22)^2 × (3^2+6^2) =

= (45^22 × 3)^2 + (45^22 × 6)^2
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g) 29^11 =29^10 × 29 =(29^5)^2 × (2^2 + 5^2)=

= (29^5 × 2)^2 + (29^5 × 5)^2
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h) 25^101 = 25^100 × 25 = (25^50)^2 × (3^2+4^2) =

= (25^50 × 3)^2 + (25^50 × 4)^2
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