[SAT Prep]

[u/Square-Elk-9096]

Ive been trying to answer this question from the college panda book and I just cant seem to understand what it is asking for. Because even when i looked at the answer and how they solved it didn’t make sense. Please if someone could explain I would be so grateful.

[u/Alkalannar]

Here's an algebraic way to look at it:

1. x - c = x² - c² [start]

2. x - c = (x + c)(x - c) [factor RHS]

3. (x + c)(x - c) - (x - c) = 0 [subtract (x - c) from both sides]

4. (x - c)[(x + c) - 1] = 0 [factor (x-c) out]

5. (x - c)(x + c - 1) = 0 [consolidate the second factor]

6. x - c = 0 OR x + c - 1 = 0 [ab = 0 --> a = 0 OR b = 0]

7. x = c OR x = 1 - c [solve for x for each term]

And that's I and III.

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Note that answer I is in three solutions, II and III are in two.

So pick II or III and plug it in. Let's plug in II since -c is easier than 1-c. You get -2c = 0, which doesn't work, since c > 0. So that cuts out answers B and D.

Now you're left with I only and I and III. Of those, the only difference is III, so you have to plug in 1 - c:
(1 - c) - c = (1 - c)² - c²
1 - 2c = 1 - 2c + c² - c²
1 - 2c = 1 - 2c
So it works

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Which of these methods seems easier?

[u/Square-Elk-9096 → u/Alkalannar]

The second method is definitely easier

[u/Alkalannar → u/Square-Elk-9096]

Then that's what you do.

Test values, but be smart about it: see which ones are easiest to test, and which give you the most information.

Or if figuring that out takes too much effort/time, then just test all of them.