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Contests
National and Regional Contests
India Contests
NMTC
2017 NMTC Junior
2
Polynomial?
Polynomial?
Source: NMTC 2017 Junior P2
October 28, 2017
algebra
polynomial
Problem Statement
If
x
,
y
,
z
,
p
,
q
,
r
x,y,z,p,q,r
x
,
y
,
z
,
p
,
q
,
r
are real numbers such that
1
x
+
p
+
1
y
+
p
+
1
z
+
p
=
1
p
\frac{1}{x+p}+\frac{1}{y+p}+\frac{1}{z+p}=\frac{1}{p}
x
+
p
1
+
y
+
p
1
+
z
+
p
1
=
p
1
1
x
+
q
+
1
y
+
q
+
1
z
+
q
=
1
q
\frac{1}{x+q}+\frac{1}{y+q}+\frac{1}{z+q}=\frac{1}{q}
x
+
q
1
+
y
+
q
1
+
z
+
q
1
=
q
1
1
x
+
r
+
1
y
+
r
+
1
z
+
r
=
1
r
.
\frac{1}{x+r}+\frac{1}{y+r}+\frac{1}{z+r}=\frac{1}{r}.
x
+
r
1
+
y
+
r
1
+
z
+
r
1
=
r
1
.
Find the numerical value of
1
p
+
1
q
+
1
r
\frac{1}{p}+\frac{1}{q}+\frac{1}{r}
p
1
+
q
1
+
r
1
.
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