00:00Given that x squared minus 4 equals 2 minus x in absolute value, what are the possible values of x?
00:06The total is being asked for, folks.
00:08Now, friends, I know that we should proceed step by step.
00:11x squared minus 4 is in absolute value if it equals 2 minus x.
00:18How could I possibly write this, guys?
00:19If I remove the negative bracket from the inside, what would this place become?
00:22Negative energy also swallows absolute value.
00:23Therefore, I can write it as x minus 2 inside an absolute value.
00:27Why did I write this?
00:28Now, let's get to this point, guys.
00:31I know that x squared minus 4 is also equal to that when it comes to factoring.
00:36The difference of two squares is x squared minus 2 squared, right guys?
00:40How can I do this?
00:42x minus 2, differences multiplied by their sums.
00:46Let's write this down too, guys.
00:48I'll write x squared minus 4 in absolute terms here.
00:53The absolute value is x minus 2 multiplied by x plus 2. These are the absolute values outside the parentheses, and if we separate them, friends...
01:04I'll do it right here.
01:06Can I write it as absolute value x minus 2 multiplied by absolute value x plus 2?
01:11What does that equal?
01:13I'll take the absolute value here.
01:15x is minus 2.
01:18Now, when I come from here, this x minus 2, guys, if you simplify it and don't count it as a cube, it's bad.
01:25Let's not do it from here.
01:26Always keep in mind that you can move this to one side or subtract the absolute value x minus 2 from both sides, or
01:33What do you do with plus absolute value minus x minus 2 from all sides, guys?
01:39Gather them.
01:40So, this is what I mean.
01:41The absolute value of x minus 2 multiplied by x plus 2 minus the absolute value of x minus 2 equals zero.
01:49This was more accurate.
01:50Okay, let's write this down now, guys.
01:52We have the absolute value of x minus 2 on all sides here, right?
01:54What were we doing, guys?
01:57We were taking our common parentheses.
01:59What happens if we factor out x minus 2 from the absolute value?
02:01The absolute value of x becomes plus 2 minus 1.
02:05That equals zero.
02:08I've been here too.
02:09Now, what does this equals zero mean?
02:10This is a multiplication situation.
02:12Either this is zero, or this is zero, or both are zero.
02:16Now, let's take a look, folks.
02:17If the absolute value of x minus 2 equals zero, then 1.
02:23What can we deduce from this, guys?
02:25The direct equation x minus equals zero requires that there be zero inside.
02:29Our x equals 2.
02:31See, that simplified expression you used already states that zero equals zero.
02:36When we get to the second one, friends.
02:39Shouldn't it be x plus 2 minus 1 equals zero here?
02:45Let me do this.
02:47Yes.
02:47I passed minus 1 to the other side.
02:49Or I added up all sides by plus 1.
02:51The absolute value of x plus 2 equals 1.
02:54What can we expect from this, guys?
02:55There are two roots, right?
02:57What does it mean for x plus 2 to equal 1 in absolute value?
03:00It's either 1 or minus 1 here.
03:01So, x plus 2 equals 1, let x be our first root, and this will be our second root.
03:08Or x plus 2 equals minus 1.
03:11Let's say we go from here to there, x 2.
03:14Please, friends?
03:15If we move the 2 to the other side, we get -2, which is equal to -1, so our x 2.
03:21Or x 3, I'll also say x 3 here with an index.
03:25If x 3 plus 2 equals zero minus 1, then our x 3 would also equal minus 3, right?
03:30Really, friends?
03:32Yes.
03:33So, that means we get 3 roots from this, folks.
03:38We were asked to add up the values of these, right guys?
03:42Yes.
03:43What does x1 plus x2 plus x3 equal, guys?
03:512 plus minus 1 plus minus 3, minus 4 goes here, 2 goes here, minus 2.
03:59Our answer is Ceyhan -2.
04:013 days.
04:015.
04:015.
04:024.
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