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3
Find particular solutions to this equation
Find particular solutions to this equation
Source:
November 25, 2019
algebra
equations
Problem Statement
Find the real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
that satisfy the following:
(i)
−
2
≤
x
≤
y
≤
z
\text{(i)} -2\le x\le y\le z
(i)
−
2
≤
x
≤
y
≤
z
(ii)
x
+
y
+
z
=
2
/
3
\text{(ii)} x+y+z=2/3
(ii)
x
+
y
+
z
=
2/3
(iii)
1
x
2
+
1
y
2
+
1
z
2
=
1
x
+
1
y
+
1
z
+
3
8
\text{(iii)} \frac{1}{x^2} +\frac{1}{y^2} +\frac{1}{z^2} =\frac{1}{x} +\frac{1}{y} +\frac{1}{z} +\frac{3}{8}
(iii)
x
2
1
+
y
2
1
+
z
2
1
=
x
1
+
y
1
+
z
1
+
8
3
Cristinel Mortici
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