Question

Resolva a equação (P+2)!/P!=72

Gab:7

Answer 1

$\frac{(p + 2)i}{pi} = 72 \\ \\ \frac{(p + 2) \times (p + 1) \times pi}{pi} = 72 \\ \\ (p + 2)(p + 1) = 72 \\ \\ p^{2} + p + 2p + 2 = 72 \\ \\ p ^{2} + 3p + 2 = 72 \\ \\ p^{2} + 3p + 2 - 72 = 0 \\ \\ p ^{2} + 3p - 72 = 0 \\ \\ aplicando \: delta \\ \\ p = \frac{ - 3 + - \sqrt{3^{2} - 4.1.( - 70)} }{2.1} \\ \\ p = \frac{ - 3 + - \sqrt{289} }{2} \\ \\ p = \frac{ - 3 + - 17}{2} \\ \\ p = 7 \\ p = 10 \\ \\ resposta \: 7 \\ \\ pois \: p = 10se \: torno \: diferente$