The sum of two number is 20.Find the numbers if the product of the square of one and the cube of the other is maximum.
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Answer:
Maximum is
19
+
√
1
=
20
→
x
=
19
,
y
=
1
Minimum is
1
+
√
19
=
1
+
4.36
=
5
(
r
o
u
n
d
e
d
)
→
x
=
1
,
y
=
19
Explanation:
Given:
x
+
y
=
20
Find
x
+
√
y
=
20
for max and min values of the sum of the two.
To obtain the max number, we would need to maximize the whole number and minimize the number under the square root:
That means:
x
+
√
y
=
20
→
19
+
√
1
=
20
→
max
[ANS]
To obtain the min number, we would need to minimize the whole number and maximize the number under the square root:
That is:
x
+
√
y
=
20
→
1
+
√
19
=
1
+
4.36
=
5
(
r
o
u
n
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