A) 1
B) 0
C) 3
D) 2
Correct Answer: B
Solution :
| [b] \[x-\sqrt{3}-\sqrt{2}=0\] \[\therefore \] \[x=\sqrt{3}+\sqrt{x}\]and \[y-\sqrt{3}+\sqrt{2}=0\] \[\therefore \] \[y=\sqrt{3}-\sqrt{2}\] Then, \[({{x}^{3}}-20\sqrt{2})-({{y}^{3}}+2\sqrt{2})\] \[={{x}^{3}}-20\sqrt{2}-{{y}^{3}}-2\sqrt{2}\] \[\Rightarrow \]\[{{x}^{3}}-{{y}^{3}}-22\sqrt{2}\]\[\Rightarrow \]\[(x-y)({{x}^{2}}+xy+{{y}^{2}})\]\[-\,22\sqrt{2}\] \[\begin{align} & =(\sqrt{3}+\sqrt{2}-\sqrt{3}+2)[(\sqrt{3}+{{\sqrt{2)}}^{2}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+(\sqrt{3}+\sqrt{2})(\sqrt{3}-2)+{{(\sqrt{3}-\sqrt{2})}^{2}}]-22\sqrt{2} \\ \end{align}\] \[=2\sqrt{2}(5+2\sqrt{6}+1+5-2\sqrt{6})-22\sqrt{2}\] \[=2\sqrt{2}(11)-22\sqrt{2}=22\sqrt{2}-22\sqrt{2}=0\] |
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