Choosing and rejecting inequality

[thomas49th]

Homework Statement

y = |(x-2)(x-4)| and y = 6 -2x

find the exact values for which these two equation equal each other

Homework Equations

The Attempt at a Solution

Right I got it down to

$$2 \pm \sqrt{2}$$ and $$4 \pm \sqrt{2}$$ and

and I've sketched the graph, however how do i work out which values to reject and which to use?

Thanks :)

 

[Mark44]

You should have two cases: one for 2 < x < 4 and the other for x < 2 or x > 4. These two cases correspond to the intervals where (x - 2)(x - 4) is negative and positive, respectively.

For the case 2 < x < 4, I solved the quadratic equation x^2 - 8x + 14 = 0. My solutions were 4 +/- sqrt(2). Since 4 + sqrt is larger than 4, it doesn't meet the restriction that 2 < x < 4, so I would discard it.

Is that enough help?

 

[thomas49th]

yes, thankyou I think I see what your saying

I will do some pratice questions

Thanks :)