Question

Determine os elementos dos conjuntos: D = { x є N | x2 = 4x – 3 }

Answer 1

$\text D = \{ \text x \in \mathbb{N}\ | \ \text x^2=4\text x-3 \ \}$

resolvendo a equação quadrática :

$\text x^2=4\text x-3$

$\text x^2-4\text x + 3 = 0$

$\text x^2-4\text x + 3 + 1 = 1$

$\text x^2-4\text x +4 = 1$

$(\text x -2)^2 = 1$

$\text x-2 = \pm 1$

$\text x = 2 \pm 1$

$\text x = 2+1 \to \text x = 3$

$\text x= 2-1 \to \text x = 1$

Portanto os elementos do conjunto do D são :

$\huge\boxed{\text D = \{\ \text x \in \mathbb{N} \ | \ \text x =3 \ \ \text{e } \ \text x = 1 \ \} }\checkmark$