Verified answer

x/q ; x ; xq.............(3)

xq*x*xq=343............(1)

x/q+x+xq=91/3........(2)

x³q/q=343

x³=343

x=7

Levando "x" em....(2)

7/q+7+7q=91/3

21+21q+21q²=91q

21q²+21q-91q+21=0

21q²-70q+21=0

Aplicando Bhaskara:

q'=3

q'=1/3

Levando em ..(3) teremos os números solicitados:

x=7

x/q=7/3

xq=7*3=21

x=7

x/q=7/1/3=7*3/1=21

x*q=7*1/3=7/3

Resposta:

7 ; 7/3 e 21

PG

u1 = u1

u2 = u1*q

u3 = u1*q²

produto

(u1*q)³ = 343 = 7³

u1*q = 7

soma

u1 + u1*q + u1*q² = 91/3

u1 + u1q² = 91/3 - 7 = 91/3 - 21/3 = 70/3

u1(1 + q²) = 70/3

u1 = 7/q

(7/q)*(1 + q²) = 70/3

7 + 7q² = 70q/3

21 + 21q² = 70q

21q² - 70q + 21 = 0

3q² - 10q + 3 = 0

delta

d² = 100 - 36 = 64

d = 8

q1 = (10 + 8)/6 = 3 --> u1 = 7/q1 = 7/3

q2 = (10 - 8)/6 = 1/3 --> u2 = 7/q2 = 21

PG (7/3, 7, 21)

PG (21, 7, 7/3)

pronto