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Chisinau City MO
1949-56 Chisinau City MO
56
Chisinau MO p56 1949-56 X system 2x2 (x+y)/xy +xy/(x+y)= a+1/a
Chisinau MO p56 1949-56 X system 2x2 (x+y)/xy +xy/(x+y)= a+1/a
Source:
March 15, 2021
algebra
system of equations
Problem Statement
Solve the system of equations
{
x
+
y
x
y
+
x
y
x
+
y
=
a
+
1
a
x
−
y
x
y
+
x
y
x
−
y
=
c
+
1
c
\begin{cases} \dfrac{x+y}{xy}+\dfrac{xy}{x+y}= a+ \dfrac{1}{a}\\ \\\dfrac{x-y}{xy}+\dfrac{xy}{x-y}= c+ \dfrac{1}{c}\end{cases}
⎩
⎨
⎧
x
y
x
+
y
+
x
+
y
x
y
=
a
+
a
1
x
y
x
−
y
+
x
−
y
x
y
=
c
+
c
1
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