Quantitative Aptitude Ques 1592
Question: If $ x=\frac{\sqrt{2}+1}{\sqrt{2}-1} $ and $ x-y=4\sqrt{2}, $ then the value of $ (x^{2}+y^{2}) $ is
Options:
A) 34
B) 38
C) 30
D) 32
Show Answer
Answer:
Correct Answer: A
Solution:
- $ x=\frac{\sqrt{2}-1}{\sqrt{2}-1} $
$ \Rightarrow $ $ x=\frac{\sqrt{2}+1}{\sqrt{2}-1}\times \frac{\sqrt{2}+1}{\sqrt{2}+1} $
$ \Rightarrow $ $ x=\frac{2+1+2\sqrt{2}}{1} $
$ \Rightarrow $ $ x=3+2\sqrt{2} $ (i) and $ x-y=4\sqrt{2} $
$ \Rightarrow $ $ y=x-4\sqrt{2} $ $ =3+2\sqrt{2}-4\sqrt{2} $ [from Eq. (i)] $ =3-2\sqrt{2} $ Now, $ x^{2}+y={{(3+2\sqrt{2})}^{2}}+{{(3-2\sqrt{2})}^{2}} $ $ =9+8+12\sqrt{2}+9+8-12\sqrt{2}=34 $
BETA
