# Greates Integer Question

• Jul 28th 2011, 07:56 PM
anshulbshah
Greates Integer Question
How to solve this question
greatest_integer(x^2) = greatest_integer(x+2)
?
• Jul 28th 2011, 07:59 PM
pickslides
Re: Greates Integer Question
You are after the largest solution to this which is also an integer?

If so solve $\displaystyle x^2-x-2 = 0$
• Jul 28th 2011, 08:10 PM
anshulbshah
Re: Greates Integer Question
No, I need all the possible values of x ( for which the eqn holds true)
• Jul 28th 2011, 08:12 PM
anshulbshah
Re: Greates Integer Question
Greatest_Integer here means the "Greatest Integer Function" ( i dont know how to express it in its form in the forum)
• Jul 28th 2011, 08:48 PM
pickslides
Re: Greates Integer Question
Quote:

Originally Posted by anshulbshah
No, I need all the possible values of x ( for which the eqn holds true)

Like this?

$\displaystyle x^2 = x+2$

$\displaystyle x^2-x-2 = 0$

$\displaystyle (x-2)(x+1) = 0$

Now use the null factor law.
• Jul 29th 2011, 01:47 PM
SammyS
Re: Greates Integer Question
Quote:

Originally Posted by pickslides
Like this?

$\displaystyle x^2 = x+2$

$\displaystyle x^2-x-2 = 0$

$\displaystyle (x-2)(x+1) = 0$

Now use the null factor law.

The two solutions that result from pickslides's post are integers, so the greatest integer function will not change them.

Now, investigate values of x very nearby these two solutions to see if they will work.