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Mathematics
Problem
Find the largest value of
k
>
0
k>0
k
>
0
for which every point satisfying
x
2
+
y
2
+
z
2
≤
k
2
x^{2}+y^{2}+z^{2}\le k^{2}
x
2
+
y
2
+
z
2
≤
k
2
also satisfies
(
x
−
3
)
2
+
y
2
+
z
2
≤
25
(x-3)^{2}+y^{2}+z^{2}\le 25
(
x
−
3
)
2
+
y
2
+
z
2
≤
25
.
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