00:01
Okay, so let's assume that the first positive real number is x.
00:09
Okay, assume first number.
00:17
Okay, this is a positive real number, is x.
00:21
And let's assume the second number is y.
00:27
So based on the condition, we know that x plus 2 times y, okay, equals s.
00:43
Okay, equals 24.
00:45
The sum is 24.
00:48
Now we want to find the two numbers which will yield the maximum product.
00:56
So we want to find p equals xy, and we want to find the maximum p.
01:04
So i can represent this product using only one variable.
01:09
Okay, let's use just y.
01:12
So i have x.
01:14
Okay, x is just 24 minus 2y.
01:21
Okay, so 24 minus 2y times y, which is minus 2y squared plus 24 times y.
01:34
So let's find the maximum value of this expression.
01:39
So we know generally if you have a quadratic equation, you can know a standard form is, okay, let's see, a times x squared plus b times x plus c...