A) 0
B) 1
C) 2
D) 4
Correct Answer: A
Solution :
Since, RHS is an even integer. Then LHS is an even integer. So, either both \[x\] and \[y\] are even integers or both of there are odd integers. Now, \[{{x}^{4}}-{{y}^{4}}=\,(x-y)(x+y)\,({{x}^{2}}+{{y}^{2}})\] \[\Rightarrow \] \[x-y,\,x+y,\,{{x}^{2}}+{{y}^{2}}\] must be an even integer. Therefore, \[(x-y)\,(x+y)\,({{x}^{2}}+{{y}^{2}})\] must be divisible by 8 and but RHS is not divisible by 8. Hence, the given equation has no solution.
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