Quantitative Aptitude Ques 1350
Question: If $ x+y=4 $ and $ \frac{1}{x}+\frac{1}{y}=4, $ then the value of $ x^{3}+y^{3} $ is
Options:
A) 52
B) 64
C) 4
D) 25
Show Answer
Answer:
Correct Answer: A
Solution:
- Given, $ x+y=4 $
(i)
and $ \frac{1}{x}+\frac{1}{y}=4 $
$ \Rightarrow $ $ \frac{y+x}{xy}=4 $
$ \Rightarrow $ $ x+y=4xy $
$ \Rightarrow $ $ 4=4xy $ [from Eq. (i)]
$ \Rightarrow $ $ xy=1 $ (ii) We know that, $ x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2}) $ $ =(x+y)[(x^{2}+y^{2})-xy] $ $ =(x+y)[{{(x+y)}^{2}}-2xy-xy] $ $ =(x+y)[{{(x+y)}^{2}}-3xy] $ $ =(4)[{{(4)}^{2}}-3\times 1] $ $ =4(16-3)=4\times 13=52 $
BETA
