Among all pairs of numbers with a sum of 238238, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Question

asked Aug 15, 2022 16.7k views

1 Answer

Victor Barrantes · Answer 1 · 2022-08-19T04:15:33+0000

Answer:

$x=119119,\;\;\;y=119119$

Explanation:

Let the
be the first number,
be the second number and
be the product of the first and second number.

i.e
x+y=238238
$\Rightarrow x=238238-y$

p=xy

$\Rightarrow p=(238238-y)y\\\Rightarrow p=238238y-y^2$

$\Rightarrow (dp)/(dy) =238238-2y\\\Rightarrow 0=238238-2y\\\Rightarrow 2y=238238\\\Rightarrow y=119119$

Now,

$x=238238-119119\\\\ \Rightarrow x=119119$

Hence,
$x=119119,\;\;\;y=119119$