SATHEE: Quantitative Aptitude Ques 821

Quantitative Aptitude Ques 821

Question: If $ x^{3}+y^{3}=9 $ and $ x+y=3, $ then the value of $ x^{4}+y^{4} $ is

Options:

A) 81

B) 32

C) 27

D) 17

Show Answer

Answer:

Correct Answer: D

Solution:

Given, $ (d)x+y=3 $ On cubing both sides, $ {{(x+y)}^{3}}=27 $ $ x^{3}+y^{3}+3xy(x+y)=27 $

$ \Rightarrow $ $ 9+3xy(3)=27 $

$ \Rightarrow $ $ 9xy=18 $
$ \Rightarrow $ $ xy=2 $ Now, $ (x+y)=3 $ On squaring both sides, $ x^{2}+y^{2}+2xy=9 $

$ \Rightarrow $ $ x^{2}+y^{2}+4=9 $

$ \Rightarrow $ $ x^{2}+y^{2}=5 $ Again, squaring both sides, $ x^{2}+y^{2}+2x^{2}y^{2}=25 $ $ x^{4}+y^{4}=25-2{{(xy)}^{2}}=25-2{{(2)}^{2}} $ $ =25-8=17 $

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Quantitative Aptitude Ques 821

Question: If $ x^{3}+y^{3}=9 $ and $ x+y=3, $ then the value of $ x^{4}+y^{4} $ is

Options:

Answer:

Solution:

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