A) 0
B) 3
C) x
D) x+3
Correct Answer: A
Solution :
[a] as \[x=\frac{1}{2+\sqrt{3}}=2-\sqrt{3}\] \[x-2=-\sqrt{3}\] Squaring both sides, we get \[{{(x-2)}^{2}}={{(-\sqrt{3})}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+4-4x=3\] \[\Rightarrow \] \[{{x}^{2}}-4x+1=0\] Now, \[{{x}^{3}}-{{x}^{2}}-11x+3={{x}^{3}}-4{{x}^{2}}+x-3{{x}^{2}}-12x+3\] \[x({{x}^{2}}-4x+1)+3({{x}^{2}}-4x+1)\] \[x\times 0+3\,\,(0)\] \[0+0=0\]
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