00:00In absolute value, x squared equals...
00:02The question asks for the product of the possible values of x, given that the absolute value of x is plus 2.
00:06Let's take a look.
00:07Now we know that, firstly, in our definition, absolute value equals x squared.
00:12Could we write something like this on our clothes?
00:13The absolute value is the square of x.
00:16We could even call it the square of fantasy.
00:18So when we write it this way, instead of absolute value x squared, it equals absolute value x squared.
00:24Can we express the absolute value as x plus 2?
00:27Yes.
00:28Now I'm going to make a change here.
00:29I'll say that the absolute value of x equals t.
00:34So, it becomes t squared equals t plus 2, right?
00:39Yes, it happened.
00:40In this case, if I move t plus 2 to this side, or subtract t plus 2 from each side, or whatever I get from each side...
00:48What am I going to do, friends?
00:49If I add -t to -2, that's this side.
00:56Wouldn't t squared minus t minus 2 equal zero?
01:00It is possible.
01:01Now, isn't this a quadratic equation with a second-degree unknown?
01:04Right, guys?
01:05Yes.
01:05Now, if I factor this, t becomes t, and this becomes 2:1.
01:11Which one should we put a minus sign on, guys?
01:12We'll put the bigger one in position 2.
01:14This will be a plus.
01:16When we multiply and add, we get minus 2t plus t minus t, which is the midpoint.
01:20t times t squared minus 2 times 1 minus 2 gave.
01:24So, we performed a correct factorization.
01:26According to this, t minus 2 times t plus 1 must equal zero.
01:33Okay friends, from what I know here, if t minus 2 equals zero, then this is the first one.
01:41Wouldn't our 't' be 2 from here?
01:43It is possible.
01:43If our value is 2, what did we define t as?
01:46Absolute value x.
01:48The absolute value of x is 2.
01:50If the absolute value is x2, then there are 2 roots here.
01:53Inside, it could be either x1 or minus 2, right?
01:57It comes out as 2.
01:58Or we can accept the inside as x2 equals 2.
02:03It can be -2, or it can be 2.
02:05Let's leave this aside for now.
02:06When we get to the second one.
02:08What was the other one, guys?
02:09The case where t plus 1 is zero.
02:12Then shouldn't our 't' be minus 1?
02:15Yes.
02:16It matched.
02:17Okay friends, since we called the absolute value of x t, the absolute value of x equals minus 1.
02:22So, could the absolute value of x be minus 1, guys?
02:24Could a statement come out as minus 1?
02:26No, it can't.
02:27Therefore, the solution set is an empty set.
02:31No roots or anything like that will come from here.
02:33So we'll take this.
02:35Our solution set here is simply -2 and 2.
02:40Their product is...
02:43x1 times x2.
02:43This outside is minus 2 times 2, which is minus 4.
02:48We say we've found the answer.
02:50Tu $1.
02:50$1.
02:50There are 5.
02:50There are 5.
02:50H palavras.
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