# Thread: x € ] - pi/4 , pi/4 ] ^ tg x = 2k(2) - 3k

1. ## x € ] - pi/4 , pi/4 ] ^ tg x = 2k(2) - 3k

Hello,
I've been having some trouble solving this problem and would like to get some help on it..
The problem is:
Verify if there is any k number that will satisfact this condition:

$\displaystyle x \in ] -\frac{\pi}{4} , \frac{\pi}{4} ] \wedge tg(x) = 2k^2 - 3k$

2. Originally Posted by misterniceguy
Hello,
I've been having some trouble solving this problem and would like to get some help on it..
The problem is:
Verify if there is any k number that will satisfact this condition:

$\displaystyle x \in ] -\frac{\pi}{4} , \frac{\pi}{4} ] \wedge tg(x) = 2k^2 - 3k$

find a value of $\displaystyle k$ that satisfies the inequality ...

$\displaystyle -1 \le 2k^2 - 3k \le 1$

3. Originally Posted by skeeter
find a value of $\displaystyle k$ that satisfies the inequality ...

$\displaystyle -1 \le 2k^2 - 3k \le 1$
Yes I actually did that, however I'm currently very poor on the inequations field...
I know this is asking for too much.. But could anyone help me solve this?

I'm in serious need here...

4. Originally Posted by misterniceguy
Yes I actually did that, however I'm currently very poor on the inequations field...
I know this is asking for too much.. But could anyone help me solve this?

I'm in serious need here...

HI

break the inequality into 2 parts ie

$\displaystyle -1\leq2k^2-3k$

$\displaystyle 2k^2-3k+1\geq0$

$\displaystyle (2k-1)(k-1)\geq0$

Try continue here .

The other parts would be

$\displaystyle 2k^2-3k\leq1$

$\displaystyle 2k^2-3k-1\leq0$

try continue here too .

after you got the solutions from the 2 parts , combine them

HI

break the inequality into 2 parts ie

$\displaystyle -1\leq2k^2-3k$

$\displaystyle 2k^2-3k+1\geq0$

$\displaystyle (2k-1)(k-1)\geq0$

Try continue here .

The other parts would be

$\displaystyle 2k^2-3k\leq1$

$\displaystyle 2k^2-3k-1\geq0$

try continue here too .

after you got the solutions from the 2 parts , combine them
Hey man thanks a lot for trying to help but.. I quit.. I just can't do anything.