greatest integer function

\hspace{-16}$Find all Real values of $\bf{x}$ that satisfy the equation\\\\ $\bf{x^2=4+[x]}$\\\\

Ans = - √2 and x = √6

I have solved it using very Lengthy Method

can anyone have a analytical Method without Using Graph

2 Answers

take :

{x}=-x²+x+4

or, 0â‰¤-x²+x+4<1. then progress.

Moreover in the Q , RHS is an Integer so L.HS.must also be an Integer.

262

Aditya Bhutra ·2012-05-16 21:50:33

clearly the roots of the eqn must lie in (-2 , 3)

and x² must be an integer .

thus x can take the values - { -âˆš2 , -1 , 0 , 1, âˆš2, âˆš3 ,2 ,âˆš5 ,âˆš6, âˆš7 ,âˆš8)

checking for the above values we get only -âˆš2 and âˆš6 as the solutions.

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