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Find two numbers differing by 38 whose product is as small as possible?

Find two numbers differing by 38 whose product is as small as possible.?How do i start this
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Dr. Juanita Wolff

Feb 20, 2025

Let the numbers are A & a+38 P=A*(A+38)=A^2 +38AP' = 2A +38for minimum p' =02A +38 =02A =-38 A =-38/2 =-19A+38 =-19+38 =19The numbers are 19 and -19... Show More
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Dr. Juanita Wolff

Feb 20, 2025

let's say one number is : x and the other one is : x + 38P = x*(x+38) = x^2 + 38 xP' = 2 x + 38P'' = 2P' = 0 ==>> 2 x + 38 = 0 => x = -38 / 2 = -19So :x = -19 , (x + 38) = -19 + 38 = 19the two numbers are -19 and 19.... Show More
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Dr. Juanita Wolff

Feb 20, 2025

What numbers are you looking for? Only Positive? It will not work.If x and x+ 38 are the numbers, you want P = x(x+38) to be minimum.So write P = x^2 + 38x = x^2 + 38x + 361 - 361 = ( x+19)^2 - 361. This is minimum if x = -19. So -19 and 19 are the numbers. Only Positive will not work.... Show More
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Dr. Juanita Wolff

Feb 20, 2025

The answer will be -(19^2) = -361. Here's how you find it:P = x(x-38) = x^2 - 38xdP/dx = 2x - 38 = 0x = 19... Show More
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Dr. Juanita Wolff

Feb 20, 2025

361 i think..x-y=38xy=f(x)y(38+y) shud b minimum,let y(38+y)=f(y)differentiate equate it to zero...get the value of y... and x and the product....... Show More
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