00:00The sum of two natural numbers whose geometric mean is 5 square root of 6 is 7.
00:04The difference is proportional to 5.
00:06The question is, what is the harmonic mean of these numbers?
00:09What's up, guys?
00:10We have two numbers whose geometric mean.
00:11Then we take it as the square root.
00:13Let's say A times B.
00:14This is equal to 5 square root of 6.
00:17Let's leave this aside.
00:18The sum of two natural numbers.
00:20A plus B.
00:22It's proportional to 7.
00:24So it's directly proportional, 7.
00:26This is equal to...
00:27I consider the differences to be A minus B.
00:29It's proportional to 5.
00:30It's also equal to that.
00:31K is proportional.
00:32Now, friends, what is it over there?
00:34First, to find the harmonic mean, we need to find A and B.
00:38If I square each side.
00:41We find that A times B is 25, and 6 times B is 150.
00:47Okay friends, here's the numerator and denominator when I add these together.
00:52A plus B plus A minus B divided by 7 plus 5.
00:57What does this equal?
00:58Wouldn't 2A divided by 12 be better?
01:00It is possible.
01:00The B's leave.
01:01So that's also equal to K.
01:03These simplify because they are in the multiplication and division case.
01:061 in 6.
01:07We find our A to be 6K from here.
01:10If it's 6K, but we substitute it here, right? So, friends, it's 5K?
01:15If we equal B from this, what do we find it to be?
01:18We find it as K.
01:19So, A is 6 times K and B is K.
01:22Back then, when we went back, we found that A multiplied by B is 150, which is the geometric mean.
01:276K squared is equal to 6K times K, which is also equal to...
01:316K squared equals 150, right guys?
01:35What is 1 da?
01:3725.
01:40Our K becomes 5 from here.
01:43Since K came out as 5, our A is 30 and our B is also 5.
01:50Now we've found them.
01:51Now we move on to the harmonic mean section.
01:531 divided by the harmonic mean.
01:55It's also equal.
01:55Since it's 1/2 of a number, what are the inverses of those numbers?
01:59The sum of the multiplicative inverses of a noun.
02:011/1 A plus 1/1 B.
02:04It's also equal to that.
02:061 divided by the harmonic mean.
02:08It's also equal.
02:081 divided by 2 times.
02:10What is 1 divided by A, guys?
02:111 in 30.
02:13What was Plus B?
02:14It was 5.
02:151 in 5.
02:16I'm setting this equal to 6.
02:18This one with 1.
02:186 plus 7.
02:20What is the harmonic mean divided by 1, guys?
02:221 divided by 2 times 7 divided by 30.
02:27Back then, 1 divided by the harmonic mean was 7 divided by 60.
02:31So what is the harmonic mean?
02:33It is 60 divided by 7.
02:35Our answer is Denizli.
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