m-p-1-a-q-p-1-r-1-b-amp-p-p-1-q-1-c-and-r-p-1-m-1-d-find-either-of-p-q-r-m-in-terms-of-a-b-c-d-

Question Number 67337 by ajfour last updated on 25/Aug/19

m (p + 1) = a

\frac{q (p + 1)}{r + 1} = b & \frac{p (p + 1)}{q + 1} = c

a n d \frac{r (p + 1)}{m + 1} = d

f i n d e i t h e r o f p, q, r, m i n t e r m s o f

a, b, c, d .

Answered by mr W last updated on 25/Aug/19

m = \frac{a}{p + 1}

q = \frac{p (p + 1)}{c} - 1

r = \frac{q (p + 1)}{b} - 1 = [\frac{p (p + 1)}{c} - 1] \frac{p + 1}{b} - 1

r (p + 1) = d (m + 1)

{[\frac{p (p + 1)}{c} - 1] \frac{p + 1}{b} - 1} (p + 1) = (\frac{a}{p + 1} + 1) d

l e t p + 1 = t

{[(t - 1) t - c] t - b c} t^{2} = (a + t) b c d

\Rightarrow t^{5} - t^{4} - {c t}^{3} - {b c t}^{2} - b c d t - a b c d = 0

\dots \dots ? ? ?

Commented by ajfour last updated on 26/Aug/19

t r y i n g a g a i n t o s o l v e t h e g e n e r a l

q u i n t i c i h a v e s t u c k u p o n t h i s S i r!

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