r-q-1-pq-q-1-c-2-p-qr-2-help-find-p-q-r-

Question Number 141246 by ajfour last updated on 17/May/21

r = q + 1

p q = q + 1

c^{2} p = {q r}^{2}, h e l p f i n d p, q, r .

Answered by Rasheed.Sindhi last updated on 17/May/21

r = p q

c^{2} p = {q r}^{2} \Rightarrow c^{2} p = q {(p q)}^{2}

\Rightarrow c^{2} p - p^{2} q^{3} = 0

p (c^{2} - {p q}^{3}) = 0

p = 0 ∣ c^{2} = {p q}^{3}

^{∙} p = 0 \Rightarrow q = - 1 \Rightarrow r = 0

(p, q, r) = (0, - 1, 0)

^{∙} c^{2} = {p q}^{3} \Rightarrow p = \frac{c^{2}}{q^{3}}

p q = q + 1 \Rightarrow (\frac{c^{2}}{q^{3}}) q = q + 1

q^{3} + q^{2} - c^{2} = 0

\dots . .