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April 6th, 2017, 05:39 AM   #1
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From: leuven

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fairly basic question regarding remarkable products

so i saw this thing in my book:

x²-2x-3=0 <-> (x²-2x+1)-1-3 = 0 <-> (x-1)²-4 = 0


So i've never seen this +1-1 thing before

When are you allowed to do this?

It seems as if they put in the +1 to get a remarkable product, I don't know the specific rules of those but why did they do this?

i saw remarkable products 5 years ago but i had some troubles back then and dropped to a lower level course where we didn't see those again. So i don't know all of the specific rules regarding remarkable products


also later on they do:

(x-1)²=4
x-1=2
or
x-1=-2
x=3
or
x=-1

Why can't they do:
(x-1)²=4
x²-1²=4
x²=4-1
x=√3

This gives a completely different result. I don't know why though
I want to be able to spot something like this myself so i'd really like to know why exactly this doesn't work.

Last edited by vlekje5; April 6th, 2017 at 05:49 AM.
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April 6th, 2017, 07:04 AM   #2
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Quote:
Originally Posted by vlekje5 View Post
Why can't they do:
(x-1)²=4
x²-1²=4
x²=4-1
x=√3
That is ENTIRELY wrong.
You need to learn the basics;
as example (x-1)^2 is NOT equal to x^2 - 1^2
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April 7th, 2017, 06:07 AM   #3
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From: leuven

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yeah you're right,

i did learn this in my first year of middle school but never had to use it since and forgot it.

Just refreshed it using a website, makes alot more sence now.

Not paying attention during math class as a kid has its downsides
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