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 $

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