Question

Aratati ca numarul a=(x - 3)² -  2 (x - 3)(x + 3) + (x + 3)² este natural ,oricare ar fii numarul real x.

Answer 1

a=X^2-6x+9-2(x^2-9)+x^2+6x+9=2x^2+18-2x^2+18=36 (ceilalti termeni se reduc)
S-au folosit formulele
(a+b)^2=a^2+2ab+b^2
(a-b)^2=a^2-2ab+b^2
(a-b)(a+b)=a^2-b^2

Answer 2

[(x-3)-(x+3)][(x-3)+(x+3)]=0  se face dupa formula a²-2ab+b²

(x-3-x-3)(x-3+x+3)=0

-6*2x=0

-12x=0

x=0 ∈N