MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1995 Swedish Mathematical Competition
3
3
Part of
1995 Swedish Mathematical Competition
Problems
(1)
a+b^2 = x+y^2 and a^2 +b = x^2 +y, if a+b+x+y < 2
Source: 1995 Swedish Mathematical Competition p3
4/2/2021
Let
a
,
b
,
x
,
y
a,b,x,y
a
,
b
,
x
,
y
be positive numbers with
a
+
b
+
x
+
y
<
2
a+b+x+y < 2
a
+
b
+
x
+
y
<
2
. Given that
{
a
+
b
2
=
x
+
y
2
a
2
+
b
=
x
2
+
y
\begin{cases} a+b^2 = x+y^2 \\ a^2 +b = x^2 +y\end {cases}
{
a
+
b
2
=
x
+
y
2
a
2
+
b
=
x
2
+
y
show that
a
=
x
a = x
a
=
x
and
b
=
y
b = y
b
=
y
algebra
system of equations
System