1. ## Absolute Value Equation

How many real numbers satisfy x^6 + |x| = 7?

Set Up:

x^6 + |x| - 7 = 0

x^6 + x - 7 = 0

Correct so far?

2. ## Re: Absolute Value Equation

Originally Posted by harpazo
How many real numbers satisfy x^6 + |x| = 7?

Set Up:

x^6 + |x| - 7 = 0

x^6 + x - 7 = 0

Correct so far?
You will actually end up with two equations. |x| is not always equal to x. For negative x we have |x| = -x.

Anyway:
For x < 0 we have $\displaystyle x^6 - x = 7$ and
For 0 < x we have $\displaystyle x^6 + x = 7$

-Dan

3. ## Re: Absolute Value Equation

Originally Posted by topsquark
You will actually end up with two equations. |x| is not always equal to x. For negative x we have |x| = -x.

Anyway:
For x < 0 we have $\displaystyle x^6 - x = 7$ and
For 0 < x we have $\displaystyle x^6 + x = 7$

-Dan
I gotta solve both equations for x. Right?

4. ## Re: Absolute Value Equation

Originally Posted by harpazo
I gotta solve both equations for x. Right?
Solving a 6th order equation is going to be problematic, to put it mildly. My suggestion would be to graph it and note how many real zeros you get. (There should be 0, 2, 4, or 6 of them.)

I realize that means the comment about the absolute value was meaningless (you can plug the absolute value into the graphing calculator) but it needed to be corrected. Graph it and see what happens.

-Dan

Thanks.