Question

Três números (x, x + 8, 25x) formam nesta ordem uma pg crescente. Determine quais são os números desta pg

Answer 1

$> resolucao \\ \\ \geqslant progressao \: geometrica \\ \\ \\ (a2) {}^{2} = (a1)(a3) \\ (x + 8) {}^{2} = (x)(25x) \\ x {}^{2} + 16x + 64 = 25 {x}^{2} \\ 25 {x}^{2} - {x}^{2} - 16x - 64 = 0 \\ 24 {x}^{2} - 16x - 64 = \div (8) \\ 3 {x}^{2} - 2x - 8 = 0 \\ \\ delta = ( - 2) {}^{2} - 4.3.( - 8) \\ delta = 4 + 96 \\ delta = 100 \\ delta = \sqrt{100} \\ delta = 10 \\ \\ \\ x = \frac{2 + 10}{6} \\ x = \frac{12}{6} \\ x = 2 \\ \\ \\ = = = = = = = = = = = = = = = = = \\ \\ \\ = x \: \: . \: \: x + 8 \: \: .25x \\ = 2 \: \: . \: \: 2 + 8 \: \: .25 \times 2 \\ = 2 \: \: . \: \: 10 \: \: . \: \: 50 \\ \\ \\ \\ pg \: > \: \: ( \: \: 2 \: \: \: . \: \: 10 \: \: . \: \: 50 \: \: ..) \\ \\ \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant$