Question

Aratati ca a este natural​

Answer 1

a = [ (7-4√3)²⁰¹³ + 1/(7+4√3)²⁰¹³ ]•(14+8√3)²⁰¹³

1/(7+4√3) = (7-4√3)/(49-16•3) =

= 7-4√3

=> 1/(7+4√3)²⁰¹³ = (7-4√3)²⁰¹³

=> a =[ (7-4√3)²⁰¹³+(7-4√3)²⁰¹³ ]•

(14+8√3)²⁰¹³

=> a = 2(7-4√3)²⁰¹³(14+8√3)²⁰¹³

=> a = 2•(7-4√3)²⁰¹³•[2(7+4√3)]²⁰¹³

=> a = 2•(7-4√3)²⁰¹³• 2²⁰¹³•(7+4√3)²⁰¹³

=> a = 2²⁰¹⁴•(7-4√3)²⁰¹³(7+4√3)²⁰¹³

=> a = 2²⁰¹⁴•[(7-4√3)(7+4√3)]²⁰¹³

=> a = 2²⁰¹⁴•(49-48)²⁰¹³

=> a = 2²⁰¹⁴•1²⁰¹³

=> a = 2²⁰¹⁴ ∈ N