Question

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.

Answer 1

Answer:

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

Step-by-step explanation:

Let the $x$ be the first number, $y$ be the second number and $p$ be the product of the first and second number.

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

      $p=xy$

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

$\Rightarrow \frac{dp}{dy} =238238-2y\\\Rightarrow 0=238238-2y\\\Rightarrow 2y=238238\\\Rightarrow y=119119$

Now,

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

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