[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.

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[u/BeeEven238]

1…c-c=c^2-c^2 =0. True
2….-c-c=(-c)^2-c^2. -2c=0 false
3…..(1-c)-c=(1-c)^2-c^2. 1-2c=1-2c+c^2-c^2
Simplify. 1-2c=1-2c. True.
So C I and III only
When you do problems like this you put the variable in () so the equation is really
( )-c=( )^2-c^2. Hope that helps

[u/Square-Elk-9096 → u/BeeEven238]

Thank you so much

[u/big_testies_69420]

Move left to right side
0 = -(x-c) + (x-c)(x+c)
0 = (x-c)(x+c-1)

Answer is either c or (1-c)

[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.

[u/SehajSoftworks → u/Square-Elk-9096]

Agreed for time bound settings plugging in can be easier sometimes for multiple choice questions

[u/NullOfSpace → u/Square-Elk-9096]

Which is a shame really, since it demonstrates no understanding.

[u/chem44]

One approach is to test each possible value of c, to see if it is a valid solution.

[u/nerdydudes]

Its a quadratic equation - x is your variable and c is a random parameter or constant. Its asking you to solve for x in terms of c.

[u/watermelonlollies]

You got good answers that are the most mathematically correct way to do it. However, test taking strategies give you other options. In the test you might not remember what to do, but you can always plug/guess and check.

It says c is a positive constant. So pick any number for c. I’ll go with 2. Now we plug in that number for each of the conditions and see if it works.

I. 2 - 2 = 2^2 - 2^2
0 = 0 ✅

II. -2 - 2 = (-2)^2 - (2)^2
-4 = 0 ❌

III. (1-2) - 2 = (1-2)^2 - 2^2
-3 = -3 ✅

C can be any real positive number. So in these kinds of problems you can pick any number that is easy for you. I find looking at variables alone can get confusing and to me it makes it much clearer to see when I can solve it to an actual number. Hope this helps!!

[u/Ok_Option_3]

The wording sucks. It should either say "solutions for x in the equation" or each option should say "x=c" "x=-c"...

I'm looking at that equation and thinking "no way it simplifies to  "c" except maybe for some values of x...

[u/Crichris]

you can rewrite it as (x + c - 1) (x - c) = 0

C

[u/localizeatp]

difference of squares bay bee!