Question

( IFRS 2018/1 ) sabendo-se que
${a}^{2} - {b}^{2} = 63$
com
$a = 3 \times x - 1$
e
$b = - x + 2$
o valor de x no conjunto dos números inteiros é:

(A) -3
(B) -1
(C) 1
(D) 2
(E) 3

Answer 1

Olá!!

De acordo com o enunciado,

$\\ \displaystyle \mathsf{a^2 - b^2 = 63} \\\\ \mathsf{(a + b)(a - b) = 63} \\\\ \mathsf{((3x - 1) + (- x + 2)) \cdot ((3x - 1) - (- x + 2)) = 63} \\\\ \mathsf{(3x - 1 - x + 2) \cdot (3x - 1 + x - 2) = 63} \\\\ \mathsf{(2x + 1) \cdot (4x - 3) = 63} \\\\ \mathsf{8x^2 - 6x + 4x - 3 = 63} \\\\ \mathsf{8x^2 - 2x - 66 = 0 \qquad \qquad \div(2} \\\\ \mathsf{4x^2 - x - 33 = 0} \\\\ \mathsf{4x^2 - 12x + 11x - 33 = 0} \\\\ \mathsf{4x(x - 3) + 11(x - 3) = 0} \\\\ \mathsf{(x - 3) \cdot (4x + 11) = 0}\\\\ \boxed{\mathsf{S = \left \{ - \frac{11}{4}, 3\right \} }}$

Logo, $\boxed{\boxed{\mathsf{x = 3}}}$, pois $\mathsf{x \in \mathbb{Z}}$.