Question

determine x a fim de que a sequencia ( x² - 4, 2x + 4, 6) seja uma P.G.

Answer 1

$\frac{2x + 4}{x^{2} - 4} = \frac{6}{2x} \\\\2x (2x + 4)= 6(x^{2}- 4) \\\\4x^{2} + 8x = 6x^{2} - 24 \\\\2x^{2} - 8x - 24=0 \\\\\Delta=(-8)^2-4*2*(-24) \\\\64+192=256 \\\\x=\frac{8(+-)\sqrt{256}}{4.4} \\\\\frac{8(+-)16}{4} \\\\x' = -2 \\\\x'' = \boxed{6}$

Resposta: x = 6

Bons estudos!