Complex Quadratic Equations

We're used to solving quadratics where we have a second degree statement. Typically what we're looking at is something. of the form AX squared plus BX plus or something like X squared minus Y squared and again we could have coefficients in here.

What we're used to doing is either factoring those or completing the square or quadratic formula, some sort of way of solving them.

But what I want to talk to you now about is what I call quadratics in disguise. And basically things that we can use those same methods to solve that don't necessarily have the same appearance as these guys. Okay.

And the first one is something of the form AX to the 2N plus BX to the N plus C is equal to 0. It's very similar to what we have up here. But we're throwing in these extra little exponents. We can actually end up factoring those just as we can something like this but instead of just using X as our first term, this is like X minus something times X plus something, we could do the same thing here but we have X to the N plus or minus something, times X to the N plus or minus something. So we can take the same exact approach that we have up here to solve something like this.

Likewise, if we have X squared minus Y squared, these don't have to necessarily be single variables. They could be, say, F of X squared minus G of X squared. The difference of two functions squared. Again, this is factored like X plus Y times X minus Y we can do the same thing here. F of X minus G of F of X. And my equal to 0.

So basically look for certain patterns that you recognize. We're used to dealing with these. These are no problem. But we can take the same approaches we use to solve them when we see a pattern and something that at least looks similar to something that we already know.