Quantitative Aptitude Ques 415
Question: If $ x+y=9 $ and $ \frac{1}{x}+\frac{1}{y}=3, $ then the value of $ x^{3}+y^{3} $ is
Options:
A) 645
B) 459
C) 729
D) 648
Show Answer
Answer:
Correct Answer: D
Solution:
- $ x+y=9 $ and $ \frac{1}{x}+\frac{1}{y}=3 $
$ \Rightarrow $ $ \frac{x+y}{xy}=3 $
$ \Rightarrow $ $ xy=\frac{x+y}{3}=\frac{9}{3}=3. $
Now, $ (x^{3}+y^{3})=(x+y)(x^{2}+y^{2}-xy) $
$ =(x+y)[{{(x+y)}^{2}}-2xy-xy] $
$ =(x+y)[{{(x+y)}^{2}}-3xy] $
$ =9,[9^{2}-3\times 3]=9,[81-9] $
$ =9\times 72=648 $
BETA
