Question

A soma de tres numeros em progressão geométrica e 26 e o produto e 216 determine esses numeros

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: geometrica \\ \\ \frac{x}{q} . x . xq = 216 \\ x {}^{3} = 216 \\ x = \sqrt[3]{216} \\ x = 6 \\ \\ = = = = = = = = = = = = = = \\ \\ \frac{x}{q} + x + xq = 26 \\ \frac{6}{q} + 6 + 6q = 26 \\ 6 + 6q + 6q {}^{2} = 26q \\ 6q {}^{2} + 6q + 6 - 26q = 0 \\ 6q {}^{2} - 20q + 6 = 0 \div (2) \\ 3q {}^{2} - 10q + 3 = 0$

$> resolvendo \: a \: equacao \: do \: 2 \: grau \\ \\ delta = ( - 10) {}^{2} - 4.3.3 \\ delta = 100 - 36 \\ delta = 64 \\ delta = \sqrt{64} \\ delta = + - 8$

$q1 = \frac{10 + 8}{6} \\ q1 = \frac{18}{6} \\ q1 = 3 \\ \\ q2 = \frac{10 - 8}{6} \\ q2 = \frac{2}{6} \\ q2 = \frac{1}{3}$

$pg > (2.6.18..) \: ou \: (18.6.2..) \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant$