The question asked "Find the sum of the solutions to $$x^2+4x+1=[x]$$ I tried solving for the sum claiming that $[x]$ was a scalar matrix, however that was incorrect. I'm not sure what $[x]$ means.
The answer was given to be $-2+\sqrt{2}$
What does [x] mean, in this context?
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linear-algebra
2 Answers
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$[x]$, in this context, seems to denote the Floor Function. The modern notation is $\lfloor x \rfloor$, but some textbooks still use the archaic notation for the floor function, which is $[x]$ as in the question. Your quadratic can be solved by bounding $x$ using a preexisting bound on the floor function, namely $$x \ge [x] > x-1$$ So this gives us a bound on $x$, which in turn restricts $[x]$. Can you take it from here?
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Basically you have to solve at first $ x \leq x^2 + 4x + 1 < x+ 1 $
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4I think this is incorrect. How is $[x] \ge x$? Try $x=3.5$. $3$ is not greater than $3.5$. What are you saying $[x]$ is? – 2017-02-05
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1I agree with @S.C.B. It should be $x-1
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0yeah sorry thats a typo – 2017-02-05