SATHEE: Quantitative Aptitude Ques 1495

Quantitative Aptitude Ques 1495

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

Options:

A) 81

B) 32

C) 27

D) 17

Show Answer

Answer:

Correct Answer: D

Solution:

If $ x^{3}+y^{3}=9 $ and $ x+y=3, $ then $ x^{4}+y^{4}=? $ Taking expression $ x+y=3 $ On cubing both sides, we get $ {{(x+y)}^{3}}={{(3)}^{3}} $

$ \Rightarrow $ $ x^{3}+y^{3}+3xy(x+y)=27 $

$ \Rightarrow $ $ 9+3xy(3)=27 $ $ {\because x^{3}+y^{3}=9andx+y=3} $

$ \Rightarrow $ $ 9xy=18 $

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

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

$ \Rightarrow $ $ x^{2}+y^{2}=5 $ $ [\because xy=2] $ Again, squaring on both sides, we get $ {{(x^{2}+y^{2})}^{2}}={{(5)}^{2}} $

$ \Rightarrow $ $ x^{4}+y^{4}+2x^{2}y^{2}=25 $

$ \Rightarrow $ $ x^{4}+y^{4}=25-2{{(xy)}^{2}} $ $ =25-2{{(2)}^{2}}=25-8=17 $

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