Question : If $x+y=5$, $x^{3}+ y^{3}=35$, what is the positive difference between $x$ and $y$?
Option 1: 0
Option 2: 1
Option 3: 5
Option 4: 6
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Correct Answer: 1
Solution :
Given: $x+y=5$ and $x^{3}+ y^{3}=35$
We know, $(x+y)^{3}=x^{3}+y^{3}+3xy(x+y)$
$⇒5^{3}=35+3xy(5)$
$⇒xy=6$
Now, $|x-y|=\sqrt{(x-y)^{2}}$
$⇒|x-y|=\sqrt{(x+y)^{2}-4xy}$
$\therefore|x-y|=\sqrt{(5)^{2}-4\times 6}=1$
Hence, the correct answer is 1.
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