Question

O resultado Y^2X^2-4a é obtido por meio de qual produtos notáveis abaixo?
a)(yx+2a)(yx-2a)
b)(yx+2a)(yx+2a)
c)(x+a)(y-2)
d)(yx+2a)^2

Answer 1

$\left(x+\frac{1}{x}\right)^2~=~12\\\\\\Desenvolvendo~o~lado~esquerdo~da~equacao,~temos:\\\\\\\left(x+\frac{1}{x}\right)~.~\left(x+\frac{1}{x}\right)~=~12\\\\\\x~.~x~+~x~.~\frac{1}{x}~+~\frac{1}{x}~.~x~+~\frac{1}{x}~.~\frac{1}{x}~=~12\\\\\\x^2~+~1~+~1~+~\frac{1}{x^2}~=~12\\\\\\x^2+\frac{1}{x^2}+2~=~12\\\\\\x^2+\frac{1}{x^2}~=~12-2\\\\\\\boxed{x^2+\frac{1}{x^2}~=~10}$

Resposta: Letra (b)