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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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