A) \[4,\,\,4\]
B) \[3,\,\,3\]
C) \[2,\,\,2\]
D) none of these
Correct Answer: A
Solution :
Given, \[{{x}^{2}}-xy+{{y}^{2}}-4x-4y+16=0\] \[\Rightarrow \] \[{{x}^{2}}-(y+4)x+{{y}^{2}}-4y+16=0\] For real \[x,\,\,{{(y+4)}^{2}}-4({{y}^{2}}-4y+16)\ge 0\] \[\Rightarrow \] \[-3{{y}^{2}}+24y-48=0\] \[\Rightarrow \] \[{{y}^{2}}-8y+16=0\] \[\Rightarrow \] \[{{(y-4)}^{2}}=0\Rightarrow y=4\] \[\therefore \] \[x=4\] \[\Rightarrow \] \[(x,\,\,y)=(4,\,\,4)\]
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