3s-2-2ps-3cp-1-0-and-3s-2p-sp-2-3cp-2-0-find-s-and-p-both-real-in-terms-of-c-R-

Question Number 79256 by ajfour last updated on 23/Jan/20

3 s^{2} - 2 p s - 3 c p - 1 = 0 a n d

3 s - 2 p - {s p}^{2} - 3 {c p}^{2} = 0

f i n d s a n d p b o t h r e a l i n t e r m s

o f c \in R .

Answered by MJS last updated on 23/Jan/20

(1) c = \frac{s^{2}}{p} - \frac{2 s}{3} - \frac{1}{3 p}

(2) c = \frac{s}{p^{2}} - \frac{s}{3} - \frac{2}{3 p}

\frac{s^{2}}{p} - \frac{2 s}{3} - \frac{1}{3 p} = \frac{s}{p^{2}} - \frac{s}{3} - \frac{2}{3 p}

3 {p s}^{2} - p^{2} s - 3 s + p = 0

s = \frac{p}{3} \lor s = \frac{1}{p}

c = - \frac{p^{2} + 3}{9 p} \lor c = \frac{1 - p^{2}}{p^{3}}

\Rightarrow

p^{2} + 9 p c + 3 = 0 \lor p^{3} + \frac{1}{c} p^{2} - \frac{1}{c} = 0

and both can be solved

Commented by mr W last updated on 24/Jan/20

m o r e t h a n f a n t a s t i c!

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