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Problems
Mathematics
Mathematics
Problem
If the lattice point
P
(
x
,
y
,
z
)
P(x, y, z)
P
(
x
,
y
,
z
)
,
x
,
y
,
z
>
0
x, y, z > 0
x
,
y
,
z
>
0
and
x
,
y
,
z
∈
I
x, y, z \in I
x
,
y
,
z
∈
I
with least value of
z
z
z
such that the 'P' lies on the planes
7
x
+
6
y
+
2
z
=
272
7x + 6y + 2z = 272
7
x
+
6
y
+
2
z
=
272
and
x
−
y
+
z
=
16
x - y + z = 16
x
−
y
+
z
=
16
, then the value of
(
x
+
y
+
z
−
42
)
(x + y + z - 42)
(
x
+
y
+
z
−
42
)
is equal to
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