Question

se (12 raiz 3;x;16 raiz 3) formam uma P.G alternada. determine x

Answer 1

$Se \ \Big(12\sqrt{3} \ ;x \ ,\ 16\sqrt{3}\Big) \ formam \ uma \ P.G. \ alternada. \ Determine \ x.\\ \\ \frac{x}{12\sqrt{3}}= \frac{16\sqrt{3}}{x} \\ \\x^2=12\sqrt{3}\cdot 16\sqrt{3}\\ \\x^2=12\cdot 16\sqrt{3 \cdot 3}\\ \\x^2=12\cdot 16\sqrt{9}\\ \\x^2=12\cdot 16\cdot3\\ \\x^2=36\cdot 16\\ \\x=\pm\sqrt{36\cdot 16}\\ \\x=\pm\sqrt{36}\cdot \sqrt{16} \\\\x=\pm6\cdot4\\ \\x=\pm24$
São duas possibilidades, porém apenas x = 24 serve.