Quantitative Aptitude Ques 1947

Question: If $ x=5, $ $ y=6 $ and $ z=-11, $ then the value of $ x^{3}+y^{3}+z^{3} $ is

Options:

A) $ -890 $

B) $ -970 $

C) $ -870 $

D) $ -990 $

Show Answer

Answer:

Correct Answer: D

Solution:

  • Given, $ x=5, $ $ y=6 $ and $ z=-11 $

$ \therefore $ $ x+y+z=5+6-11 $

$ \Rightarrow $ $ x+y+z=0 $ … (i) Now, $ x^{3}+y^{3}+z^{3}-3xyz $ $ =(x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-xz) $

$ \Rightarrow $ $ x^{3}+y^{3}+z^{3}-3xyz=0 $ [from Eq. (i)]

$ \Rightarrow $ $ x^{3}+y^{3}+z^{3}=3xyz $

$ \Rightarrow $ $ x^{3}+y^{3}+z^{3}=3(5)(6)(-11) $

$ \therefore $ $ x^{3}+y^{3}+z^{3}=-990 $

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