00:00The arithmetic mean of A and B is 3.
00:02What is the number whose geometric mean is 2√3 and whose geometric mean is 3√2 and whose geometric mean is the same as B?
00:07That's what he asks us in our question.
00:09Now, friends, if the arithmetic mean of A and B is 3, can we find the sum of A plus B?
00:13Yes.
00:13A plus B divided by 2 equals 3.
00:15When we multiply A plus B, which equals 2 times 3, we get 6.
00:19So, what about A, which has a geometric mean of 2 square root of 3, and B, which has a geometric mean of 3 square root of 2?
00:25Let our number be x.
00:27In this case, when we take the square root of A times x, we get the geometric mean.
00:32That would also equal 2 square root of 3, and B times x, which equals 3 square root of 2, wouldn't it?
00:40It is possible.
00:40If I square both sides and then square both sides and it equals, what does that equal, guys?
00:48Since A times x gets rid of the square root, A times x equals 12.
00:52B times x equals 18.
00:55I'll need to collect these side by side, guys.
00:59I write A plus B in parentheses X.
01:02That equals 30, right guys?
01:05Yes.
01:05What was the sum of A plus B? Initially, it was 6.
01:08So, if 6 times x equals 30, then we find our x to be 5.
01:13We say the answer is C is equal to B.
Yorumlar