00:00Given that the geometric mean of A and 2B is 1
00:02The question asks what the product of A squared plus 1 divided by B squared multiplied by B squared plus 1 divided by A squared is.
00:07That's our question, friends.
00:08Now, friends, what is the geometric mean of A and 2B?
00:12The square root of A multiplied by 2B equals... what is that? 1, folks.
00:17So, can I find the square root of AB from here? Yes, I can.
00:21So I find it as 1 divided by the square root of 2, right guys?
00:24Yes, if I square these, let's have them on hand.
00:29A times B equals 1 divided by 2, right guys?
00:33So, when we get to this point, the equation we're asked for is A squared times B squared, right friends?
00:39Excuse me, isn't it A squared plus 1 divided by B squared times B squared plus 1 divided by A squared?
00:44Okay, so when I elaborate a bit, it's A squared times B squared plus 1 divided by, right?
00:51When we convert this to a full fraction, we get an improper fraction divided by B squared multiplied by...
01:00As it appears, A squared times B squared plus 1 divided by...
01:03We multiply these two together, and then we add them together.
01:05We multiply the two and then add them.
01:07Divided by A squared.
01:09That's equal to A squared times B squared.
01:10Now we've found the EU, which is A times B.
01:12What is A squared times B squared?
01:15It is 1/4.
01:17When we square both of them.
01:20What's going on here, guys?
01:211/4 plus 1/B squared times 1/4 plus 1/A squared.
01:30It's also equal to that.
01:321 in 4.
01:334 squares 4.
01:34Another 5 divided by 4.
01:36Here, 5 divided by 4.
01:39What was A squared times B squared, guys?
01:411 in 4.
01:43Isn't it?
01:44Yes.
01:44I connected the fraction lines.
01:46It's also equal to that.
01:4825 divided by 16 multiplied by 4 is also equal to 4.
01:51We get our answer, 25 divided by 4, when the following simplifies.
01:55The answer is 25 divided by 4.
01:57We're talking about Bolu.
01:57Thank you for combining them.
01:57Thank you for combining them.
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