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Question Number 88329 by TawaTawa1 last updated on 10/Apr/20

Commented by TawaTawa1 last updated on 10/Apr/20

$Find x, y and z$
Commented by Tony Lin last updated on 10/Apr/20

${\begin{cases} x = \frac{2 p q}{q + p - r} \\ y = \frac{2 q r}{q + r - p} o r \\ z = \frac{2 p r}{p + r - q} \end{cases}$ ${\begin{cases} x = 0 \\ y = 0 \\ z = 0 \end{cases}$
Commented by Tony Lin last updated on 10/Apr/20

$y z - q z = p y$ $z = \frac{p y}{y - q}$ $x y - r x = p y$ $x = \frac{p y}{y - r}$ $\frac{p^{2} y^{2}}{(y - r) (y - q)} = \frac{p q y}{y - q} + \frac{p r y}{y - r}$ $p^{2} y^{2} = p q y (y - r) + p r y (y - q)$ $i f p, y \neq 0$ $p y = q y - q r + r y - r q$ $y = \frac{2 q r}{q + r - p}$ $x = \frac{p y}{y - r} = \frac{2 p q}{q + p - r}$ $z = \frac{p y}{y - q} = \frac{2 p r}{p + r - q}$ $i f y = 0$ $t h e n x, z = 0$ $s i m i l a r i l y$ $i f x = 0$ $t h e n y, z = 0$ $i f z = 0$ $t h e n x, y = 0$ $i f o n e o f p, q, r = 0 o r m o r e$ $t h e n t h e e q u a t i o n h a s \infty s o l u t i o n$
Commented by TawaTawa1 last updated on 10/Apr/20

$God bless you sir .$
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