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2022-23 IOQM India
16
IOQM 2022-23 P-16
IOQM 2022-23 P-16
Source:
October 30, 2022
algebra
IOQM
system of equations
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be reals satisfying\\
3
a
b
+
2
=
6
b
,
3
b
c
+
2
=
5
c
,
3
c
a
+
2
=
4
a
.
\hspace{2cm} 3ab+2=6b, \hspace{0.5cm} 3bc+2=5c, \hspace{0.5cm} 3ca+2=4a.
3
ab
+
2
=
6
b
,
3
b
c
+
2
=
5
c
,
3
c
a
+
2
=
4
a
.
\\ \\ Let
Q
\mathbb{Q}
Q
denote the set of all rational numbers. Given that the product
a
b
c
abc
ab
c
can take two values
r
s
∈
Q
\frac{r}{s}\in \mathbb{Q}
s
r
∈
Q
and
t
u
∈
Q
\frac{t}{u}\in \mathbb{Q}
u
t
∈
Q
, in lowest form, find
r
+
s
+
t
+
u
r+s+t+u
r
+
s
+
t
+
u
.
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