Explicație pas cu pas:
Notam a = 3k, b = 4k, c = 5k
a)
[tex] a^2 + b^2 = (3k)^2 + (4k)^2 = 9k^2 + 16k^2 = 25k^2 = (5k)^2 [/tex] patrat perfect
b) [tex] 2b(a + c) = 256 => b(a + c) = 128 => 4k(3k + 5k) = 128 => 4k * 8k = 128 => 32k^2 = 128 => k^2 = 4 => k = {-2, 2}[/tex]
Daca a,b,c sunt naturale => k = 2
a = 6, b = 8, c = 10
Daca a,b,c sunt intregi => k = {-2, 2}
solutia 1: a = -6, b = -8, c = -10
solutia 2: a = 6, b = 8, c = 10
