$(a+b+c-x)$ $\left| {\,\begin{array}{*{20}{c}}
1&c&b \\
1&{b - x}&a \\
1&a&{c - x}
\end{array}\,} \right|\, = 0$
=> $(a+b+c-x)$ $[{(b-x)(c-x)-a^2}$ $ + c(a-c+x) + {b({a-b+x)}}] =0$
=> $(a+b+c-x)$ $[(bc-cx+bx+x^2-a^2 + ca - c^2 + cx +ab -b^2 +bx] =0$
==> $(a+b+c)[x^2 -(a^2+b^2+c^2)+ab+bc+ca]=0$
$(a+b+c-x)[x^2-(a^2 + b^2 +c^2] = 0$
[ $\because$ $ab + bc + ca = 0$]
$x=a+b+c $ and $(a^2+b^2+c^2)^{1/2} $
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$f\left( x \right) = \left\{ \begin{gathered} x{\left\{ x \right\}^2},x \notin I \hfill \\ x\,\,\,\,\,\,\,\,\,\,,x \in I \hfill \\ \end{gathered} \right.,$
હોય તો નિચેનામાંથી ક્યુ સાચુ છે ?
(જ્યા $\{.\}$ એ અપૂર્ણાક વિધેય છે)