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 $

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