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India IOQM
2022 IOQM India
6
IOQM 2022 P6
IOQM 2022 P6
Source:
March 8, 2022
IOQM
Problem solving strategies
folklore
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive real numbers such that
x
2
+
y
2
=
49
,
y
2
+
y
z
+
z
2
=
36
x^2 + y^2 = 49, y^2 + yz + z^2 = 36
x
2
+
y
2
=
49
,
y
2
+
yz
+
z
2
=
36
and
x
2
+
3
x
z
+
z
2
=
25
x^2 + \sqrt{3}xz + z^2 = 25
x
2
+
3
x
z
+
z
2
=
25
. If the value of
2
x
y
+
3
y
z
+
z
x
2xy + \sqrt{3}yz + zx
2
x
y
+
3
yz
+
z
x
can be written as
p
q
p \sqrt{q}
p
q
where
p
,
q
∈
Z
p,q \in \mathbb{Z}
p
,
q
∈
Z
and
q
q
q
is squarefree, find
p
+
q
p+q
p
+
q
.
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