Solve-x-y-and-z-in-terms-of-p-q-and-r-yz-py-qz-i-zx-qz-rx-ii-xy-rx-py-iii-

Question Number 11268 by tawa last updated on 18/Mar/17

Solve x, y and z in terms of p, q and r

yz = py + qz \dots \dots . . (i)

zx = qz + rx \dots \dots . (ii)

xy = rx + py \dots \dots . (iii)

Answered by mrW1 last updated on 18/Mar/17

(i i i) \Rightarrow y = \frac{r x}{x - p}

(i) \Rightarrow z = \frac{p y}{y - q} = \frac{p}{1 - \frac{q}{y}} = \frac{p}{1 - \frac{q (x - p)}{r x}}

(i i) \Rightarrow z = \frac{r x}{x - q}

\Rightarrow \frac{r x}{x - q} = \frac{p}{1 - \frac{q (x - p)}{r x}}

r x [1 - \frac{q (x - p)}{r x}] = p (x - q)

r x - q (x - p) = p (x - q)

(p + q - r) x = 2 p q

\Rightarrow x = \frac{2 p q}{p + q - r}

s i m i l a r l y

\Rightarrow y = \frac{2 q r}{q + r - p}

\Rightarrow z = \frac{2 p r}{p + r - q}

Commented by tawa last updated on 18/Mar/17

God bless you sir . i really appreciate .

Commented by tawa last updated on 18/Mar/17

please sir . i need the cubic equation formulars you posted sometimes ago .

Commented by mrW1 last updated on 18/Mar/17

Commented by tawa last updated on 18/Mar/17

God bless you sir .

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 19/Mar/17

t h e s y s t e m o f t h i s e q u a t i o n s h a v e o n e

m o r e a n s w e r s : x = y = z = 0

Commented by mrW1 last updated on 19/Mar/17

y o u a r e r i g h t . t h i s c a s e s h o u l d b e c o n s i d e r e d

i n t h e s t e p 2 .

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