Question

Exercitiul doi ......

Answer 1

n²-2n+16 = patrat perfect
n²-2n+16 =x² 
x²-n²=16-2n
(x+n)(x-n) = 16-2n =1×2(8-n)
x+n = 2       x = 2-n 
x-n = 8-n     x = 8    2-n = 8   n =-6
n² - 2n + 16 = (-6)² - 2×(-6)+16 = 36 +12+16 =64= (8)² = p.p.

x-n = 2       x = 2+n 
x+n =8-n     x = 8-2n    2+n = 8-2n   3n = 6    n=2

n² - 2n + 16 = (2)² - 2×(2)+16 = 4 -4+16 =16= (4)² = p.p.

-2n+16=0   ⇒ n= 8
n² - 2n + 16 = (8)² - 2×(8)+16 = 64 -16+16 =64= (8)² = p.p.

raspuns : n ∈ {-6,2,8}