Quantitative Aptitude Ques 107
Question: Let $ x=\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}} $ and $ y=\frac{1}{x}, $ then the value of $ 3x^{2}-5xy+3y^{2} $ is
Options:
A) 1771
B) 1177
C) 1717
D) 1171
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ x=\frac{\sqrt{3}+\sqrt{11}}{\sqrt{13}-\sqrt{11}} $ and $ y=\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}} $ $ [ \because y=\frac{1}{x} ] $
$ \therefore $ $ x+y=\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}+\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}} $ $ =\frac{{{(\sqrt{13}+\sqrt{11})}^{2}}+{{(\sqrt{13}-\sqrt{11})}^{2}}}{{{(\sqrt{13})}^{2}}+{{(\sqrt{11})}^{2}}} $ $ =\frac{2[,{{(\sqrt{13})}^{2}}+{{(\sqrt{11})}^{2}}]}{13-11}=13+11=24 $
$ \therefore $ $ 3x^{2}-5xy+3y^{2}=3,{{(x+y)}^{2}}-11xy $ $ =3,{{(24)}^{2}}-11=1717 $
BETA
