00:01
Hi, let's start the solution.
00:02
Question says that the product of two positive number is 54.
00:06
So now let a and b be two numbers whose product is 54.
00:23
So that is a into b is equal to 54.
00:28
So b equal to 54 upon a.
00:33
And then question says that the numbers is that the numbers is equal to 54.
00:37
The sum of the first number plus square of the second number is as small as possible.
00:42
So now let function f be sum of first term that is a and square of second term that is b square.
00:55
So we get here f of a is a plus b square that is a plus b is 54 square upon a square.
01:06
So it can be written as a plus 50.
01:08
4 square is 2916 into 1 upon a square that is f of a so we have to find these numbers a and b so that function f as small as possible so let's compute relative minimum of function f of function f.
01:39
So now differentiate f of a with respect to a.
01:42
We get f -dash a differentiation of a with respect to a is 1 plus 2916 as it is.
01:50
Differentiation of 1 upon a square is minus 2 upon a cube.
01:54
So here we get 1 minus 2196 2916 into 2 gives 5 8 3 2 upon a cube.
02:02
So now put f .dor 6 .916 into 2 gives 5883 2 upon a cube.
02:04
So now put f.
02:08
Dash a equal to 0 so we get here 1 minus 5 8 3 2 upon a cube is 1 so that means here we get 5 8 3 2 upon a cube equal to 1 so that means we have a cube is equal to 5 8 3 2 and a cube is that is the cube of 18 so by comparing here we get a is 18 so if a is 18 so if a is 18 then b is 54 upon a that is 54 upon 18 that gives 3...
