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$[x]^2-7[x]+12=0$

find $x$? where $[x]$ is Greatest Integer function

I have tried to solve the question like this: putting $[x]=y$ , we have the equation: $y^2-7x+12=0$ by solving this equation we get $y=3$ and $y=4$

since $y=[x]$, therefore $[x]=3$ and $[x]=4$

according to the above statement we can say that $x=[3,5)$

I want to know weather my solution is correct or not. and if it not correct then how to solve this equation.

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1 Answer 1

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For all real numbers, $x$, the greatest integer function returns the largest integer less than or equal to $x$. In essence, it rounds down a real number to the nearest integer.

For example: $$[1] = 1 , [1.5] = 1,[3.7] = 3 ,[4.3] = 4$$

Computer scientists refers to it as the floor function.

Now,Your answer is totally right. because $[3.1] = 3, [3.9] =3,[4.9] = 4$

And so you are right at concluding that $x \in [3,5)$ but beaware you shouldn't say that $x = [3,5)$, you have to use belongs here so it is more correct to say $x \in [3,5)$

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