Solve for x- p-q-xr -q-r-xp - r-p-xq -4xp-q-r -1

#160; #10; #10;The given equation can #10;be re written as #10; p+q xr+1 +q+r xp +1 + r+p xq+ #10;1 = 4 4xp+q+r #10;or #160; #1 ...

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Linear Equation in One Variable

Solve for x: ...

Question

Solve for x: $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{4 x}{p + q + r}$ =1

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Solution

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\frac{(x + q) (x + r)}{(q - p) (r - p)} + \frac{(x + r) (x + p)}{(r - q) (p - q)} + \frac{(x + p) (x + q)}{(p - r) (q - r)} - 1 = 0

p, q, r

y = \frac{1}{1 + x^{q - p} + x^{r - p}} + \frac{1}{1 + x^{r - q} + x^{p - q}} + \frac{1}{1 + x^{p - r} + x^{q - r}}

\frac{d y}{d x} =

\times

(p - q) x + (q - r) y + (r - p) = 0

(q - r) x + (r - p) y + (p - q) = 0

(r - p) x + (p - q) y + (q - r) = 0

$I f P (Q - r) x^{2} + Q (r - P) x + r (P - Q) = 0 h a s e q u a l r o o t s t h e n \frac{2}{Q} = (w h e r e P, Q, r ϵ R)$

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