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ધારો કે $a ,b ,c $ માટે $b + c \ne 0$ . જો $\left| {\begin{array}{*{20}{c}}a&{a + 1}&{a - 1}\\{ - b}&{b + 1}&{b - 1}\\c&{c - 1}&{c + 1}\end{array}} \right| + \left| {\begin{array}{*{20}{c}}{a + 1}&{b + 1}&{c - 1}\\{a - 1}&{b - 1}&{c + 1}\\{{{\left( { - 1} \right)}^{n + 2}} \bullet a}&{{{\left( { - 1} \right)}^{n + 1}} \bullet b}&{{{\left( { - 1} \right)}^n} \bullet c}\end{array}} \right| = 0$ તો $n$ મેળવો.
$0$
યુગ્મ પૂર્ણાંક
અયુગ્મ પૂર્ણાંક
પૂર્ણાંક
Solution
$\left| {\begin{array}{*{20}{c}}
a&{a + 1}&{a – 1}\\
{ – b}&{b + 1}&{b – 1}\\
c&{c – 1}&{c + 1}
\end{array}} \right| + \left| {\begin{array}{*{20}{c}}
{{{\left( { – 1} \right)}^{n + 2}}a}&{a + 1}&{a – 1}\\
{{{\left( { – 1} \right)}^{n + 1}}b}&{b + 1}&{b – 1}\\
{{{\left( { – 1} \right)}^n}c}&{c – 1}&{c + 1}
\end{array}} \right|$
$ = \left| {\begin{array}{*{20}{c}}
{a + {{\left( { – 1} \right)}^{n + 2}}a}&{a + 1}&{a – 1}\\
{ – b + {{\left( { – 1} \right)}^{n + 1}}b}&{b + 1}&{b – 1}\\
{c + {{\left( { – 1} \right)}^n}c}&{c – 1}&{c + 1}
\end{array}} \right|$
$=0$ if $n$ is an obb integer.
