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Determine the value of the sum of all elements of the set $A=\{ x \in \Bbb R | \frac{3x^2+5x+2}{x^2+x+1}\in \Bbb N\}$

I proceeded as follows: (I am assuming that $0$ is natural, but this will not affect the approach) Find all natural numbers $k$ such that $f(x)=\dfrac{3x^2+5x+2}{x^2+x+1} = k$ for $x\in \mathbb{R}$. ...
Sam's user avatar
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1 vote
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Determine the value of the sum of all elements of the set $A=\{ x \in \Bbb R | \frac{3x^2+5x+2}{x^2+x+1}\in \Bbb N\}$

The solution of @Sam is good. It's just another viewpoint one can see. Observe that, $\dfrac{3x^2+5x+2}{x^2+x+1} = 3 + \dfrac{2x-1}{x^2+x+1} \in \mathbb N \iff \dfrac{2x-1}{x^2+x+1} \geq -2$. That is $...
Afntu's user avatar
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