if X+y=10,find the minimum value of X2+y2.
Answers
Answer:
Answer
x
Explanation:
Given:
2
x
+
y
=
10
We can rewrite in terms of
y
as
y
=
10
−
2
x
Now substitute
x
2
+
y
2
x
2
+
(
10
−
2
x
)
2
x
2
+
100
−
40
x
+
4
x
2
Call the value of this expression
A
.
A
=
5
x
2
−
40
x
+
100
We notice that
A
is a parabola that opens upwards. So to find our minimum we can use differentiation.
A
'
=
10
x
−
40
The minimum will occur when the derivative equals
0
.
0
=
10
x
−
40
0
=
10
(
x
−
4
)
x
=
4
Therefore, the minimum value will occur when
y
=
2
and
x
=
4
. This means the minimum value is
2
2
+
4
2
=
20
Hopefully this helps!
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Answer:
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