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Mathematics
Mathematics
Problem
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive real numbers such that
p
=
a
2
b
+
a
b
2
−
a
2
c
−
a
c
2
p = a^2b + ab^2 - a^2c - ac^2
p
=
a
2
b
+
a
b
2
−
a
2
c
−
a
c
2
;
q
=
b
2
c
+
b
c
2
−
a
2
b
−
a
b
2
q = b^2c + bc^2 - a^2b - ab^2
q
=
b
2
c
+
b
c
2
−
a
2
b
−
a
b
2
and
r
=
a
c
2
+
a
2
c
−
c
b
2
−
b
c
2
r = ac^2 + a^2c - cb^2 - bc^2
r
=
a
c
2
+
a
2
c
−
c
b
2
−
b
c
2
and the quadratic equation
p
x
2
+
q
x
+
r
=
0
px^2 + qx + r = 0
p
x
2
+
q
x
+
r
=
0
has equal roots; then
a
,
b
,
c
a, b, c
a
,
b
,
c
are in : (a) A.P (b) G.P (c) H.P (d) None of these
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