A) 1771
B) 1177
C) 1717
D) 1171
Correct Answer: C
Solution :
| [c] \[x=\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}=\frac{{{(\sqrt{13}+\sqrt{11})}^{2}}}{{{(\sqrt{13})}^{2}}-{{(\sqrt{11})}^{2}}}\] \[=\frac{13+11+2\sqrt{13}\sqrt{11}}{13-11}=\frac{24+2\sqrt{143}}{2}=12+\sqrt{143}\] \[y=\frac{1}{x}=\frac{1}{12+\sqrt{143}}=\frac{12-\sqrt{143}}{{{(12)}^{2}}-{{(\sqrt{143})}^{2}}}=\frac{12-\sqrt{143}}{144-143}=12-\sqrt{143}\] \[\therefore \] \[3{{x}^{2}}-5xy+3{{y}^{2}}=3\,{{(12+\sqrt{143})}^{2}}-5\,(12+\sqrt{143})\] \[(12-\sqrt{143})+3\,{{(12-\sqrt{143})}^{2}}\] \[=3\,(144+143+24\sqrt{3})-5\,(144-143)+\,3\,(144+143-24\sqrt{3})\]\[=3\times 287+3\times 24\sqrt{3}-5+3\times 287-3\times 24\sqrt{3}\] \[=1722-5=1717\] |
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