1. ## Greates Integer Question

How to solve this question
greatest_integer(x^2) = greatest_integer(x+2)
?

2. ## Re: Greates Integer Question

You are after the largest solution to this which is also an integer?

If so solve $\displaystyle \displaystyle x^2-x-2 = 0$

3. ## Re: Greates Integer Question

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

4. ## 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)

5. ## Re: Greates Integer Question

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

$\displaystyle \displaystyle x^2 = x+2$

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

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

Now use the null factor law.

6. ## Re: Greates Integer Question

Originally Posted by pickslides
Like this?

$\displaystyle \displaystyle x^2 = x+2$

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

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

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.