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Question: Answered & Verified by Expert
Let $x, y, z$ be positive reals. Which of the following implies $x=y=z$ ?
MathematicsBasic of MathematicsKVPYKVPY 2015 (SA)
Options:
  • A $x^{3}+y^{3}+z^{3}=3 x y z$
  • B $x^{3}+y^{2} z+y z^{2}=3 x y z$
  • C $x^{3}+y^{2} z+z^{2} x=3 x y z$
  • D $\quad(x+y+z)^{3}=27 x y z$
Solution:
1808 Upvotes Verified Answer
The correct answer is: $x^{3}+y^{2} z+y z^{2}=3 x y z$
For option (3) if $x=z=1$ and $y=2$ then option (3) is right.
So by option (3) we can't say $x=y=z$. Remaining options implies $x=y=z$

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