A) 2
B) 1
C) 8
D) 0
Correct Answer: A
Solution :
\[{{n}^{4}}-6{{n}^{2}}+25={{n}^{4}}+10{{n}^{2}}+25-16{{n}^{2}}\] |
\[=({{n}^{2}}+5-4n)({{n}^{2}}+5+4n)\] |
Since \[{{n}^{4}}-6{{n}^{2}}+25\]is prime, |
\[\therefore \] either \[{{n}^{2}}+5-4n=1\] i.e. \[n=2\] |
or \[{{n}^{2}}+5+4n=1\] i.e. \[n=-2\] |
\[\therefore \] Number of integral solutions is 2. |
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