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 $
BETA
