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Nordic
1992 Nordic
1
1
Part of
1992 Nordic
Problems
(1)
find x_i, i=1,2,3 if Σx_i+Σ3/(x_i-1)-2Σ\sqrt{x_i+2}=0
Source: Nordic Mathematical Contest 1992 #1
10/5/2017
Determine all real numbers
x
>
1
,
y
>
1
x > 1, y > 1
x
>
1
,
y
>
1
, and
z
>
1
z > 1
z
>
1
,satisfying the equation
x
+
y
+
z
+
3
x
−
1
+
3
y
−
1
+
3
z
−
1
=
2
(
x
+
2
+
y
+
2
+
z
+
2
)
x+y+z+\frac{3}{x-1}+\frac{3}{y-1}+\frac{3}{z-1}=2(\sqrt{x+2}+\sqrt{y+2}+\sqrt{z+2})
x
+
y
+
z
+
x
−
1
3
+
y
−
1
3
+
z
−
1
3
=
2
(
x
+
2
+
y
+
2
+
z
+
2
)
algebra
equation