Answered

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The sum of the first number squared and the second number is 51 and the product is a maximum.

Sagot :

Answer:

Step-by-step explanation:

To find the two numbers

x and

y such that the sum

2

+

x

2

+y is 51 and the product

xy is maximized, we can use the method of substitution and optimization.

Let's denote

=

51

−

2

y=51−x

2

, since

2

+

=

51

x

2

+y=51. Now, we need to maximize the product

=

(

51

−

2

)

xy=x(51−x

2

).

Let's find the derivative of

xy with respect to

x:

=

51

−

3

xy=51x−x

3

(

)

=

51

−

3

2

dx

d(xy)

​

=51−3x

2

Setting the derivative equal to zero to find critical points:

51

−

3

2

=

0

51−3x

2

=0

3

2

=

51

3x

2

=51

2

=

17

x

2

=17

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