Answer:
Step-by-step explanation:
<em>Let one number = x
</em>
<em>Let the other number = y
</em>
<em> </em>
<em>x + y = 9
</em>
<em> </em>
<em>xy2 is a maximum
</em>
<em> </em>
<em> </em>
<em>Since we need positive numbers, we assign values of x and y respectively that will give us a sum of 9.
</em>
<em> </em>
<em>x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
</em>
<em> </em>
<em>y: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
</em>
<em> </em>
<em> </em>
<em>Next, we square the values of y.
</em>
<em> </em>
<em>y2: 81, 64, 49, 36, 25, 16, 9, 4, 1, 0
</em>
<em> </em>
<em> </em>
<em>Next, we multiply x by y2 to see which product is the highest value.
</em>
<em> </em>
<em>x : 0 , 1 , 2 , 3 , 4 , 5 , 6, 7, 8, 9
</em>
<em>y2 : 81, 64, 49, 36, 25, 16, 9, 4, 1, 0
</em>
<em> </em>
<em> </em>
<em>We can eliminate x = 0, x = 8 , and x = 9 , since the product of xy2 is of lowest value.
</em>
<em> </em>
<em>1 x 64 = 64
</em>
<em>2 x 49 = 92
</em>
<em>3 x 36 = 108
</em>
<em>4 x 25 = 100
</em>
<em>5 x 16 = 80
</em>
<em>6 x 9 = 54
</em>
<em>7 x 4 = 28
</em>
<em> </em>
<em>The highest product value here is 108. </em>
<em> </em>
<em>The two numbers in the solution are 3 and 6.</em>
