Quantitative Aptitude Ques 579
Question: If $ x=3+2\sqrt{2}, $ then the values of $ x^{3}+\frac{1}{x^{3}} $ and $ x^{3}-\frac{1}{x^{3}} $ are respectively.
Options:
A) $ 140\sqrt{2}, $ 198
B) 234, 216
C) 216, 234
D) 198, $ 140\sqrt{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ x=3+2\sqrt{2} $ $ x+\frac{1}{x}=3+2\sqrt{2}+\frac{1}{3+2\sqrt{2}}\times \frac{(3-2\sqrt{2})}{(3-2\sqrt{2})} $ $ =3+2\sqrt{2}+\frac{3-2\sqrt{2}}{9-8}=3+2\sqrt{2}+3-2\sqrt{2} $
$ \Rightarrow $ $ x+\frac{1}{x}=6 $ On cubing both sides, we get $ x^{3}+\frac{1}{x^{3}}+3( x+\frac{1}{x} )x\times \frac{1}{x}=6^{3} $
$ \Rightarrow $ $ x^{3}+\frac{1}{x^{3}}+3,(6)=216 $
$ \Rightarrow $ $ x^{3}+\frac{1}{x^{3}}=216-18=198 $ Similarly, $ x^{3}-\frac{1}{x^{3}}=140\sqrt{2} $
BETA
