Question

Multumesc anticipat!

Answer 1

Răspuns:

asa este!!

Explicație pas cu pas:

2007*2009*2015*2017+64=(2012-3) (2012+3) (2012-5) (2012+5)+64=

(2012²-9) (2012²-25)+64=

2012^4-34*2012²+225+64=

2012^4-34*2012²+289=

(2012²-17)²care e p.p

deci √(2012²-17)²=2012²-17∈N

Answer 2

$\ir Not\breve{a}m\ 2007=a,\ iar\ produsul\ de\ sub\ radical\ devine:\\ \\ a(a+2)(a+8)(a+10)=[a(a+10)][(a+2)(a+8)]=(a^2+10a)(a^2+10a+16)\\ \\ Not\breve{a}m\ a^2+10a = b,\ iar\ expresia\ de\ sub\ radical\ devine:\\ \\ b(b+16)+64=b^2+16b+8^2 =(b+8)^2$

Prin urmare, sub radical avem un pătrat perfect, deci A∈ ℕ.