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સમીકરણ $\frac{{p + q - x}}{r} + \frac{{q + r - x}}{p}\,\, + \,\,\frac{{r + p - x}}{q}\,\, + \;\,\frac{{4x}}{{p + q + r}} = 0$ ને ઉકેલ........છે
$x = p + q + r$
$x = p - q + r$
$x = \frac{{p + q}}{{q + r}}$
$x = \frac{p}{q} + r$
Solution
$\frac{{p + q – x}}{r} + \frac{{q + r – x}}{p} + \frac{{r + p – x}}{q}\,\, = \,\,\frac{{ – 4x}}{{p + q + r}}\,$ સમીકરણ આપેલ છે.
$\frac{{p + q + r – x}}{r} + \frac{{p + q + r – x}}{p} + \frac{{p + q + r – x}}{q} = \,\,4 – \frac{{4x}}{{p + q + r}}$
$(p + q + r – x)\,\left( {\frac{1}{p} + \frac{1}{q} + \frac{1}{r}} \right) = 4\,\left( {\frac{{p + q + r – x}}{{p + q + r}}} \right)$
$ \Rightarrow \,\,(p + q + r – x)\,\left[ {\frac{1}{p} + \frac{1}{q} + \frac{1}{r} – \frac{4}{{p + q + r}}} \right] = 0$
$ \Rightarrow \,\,x = p + q + r$
