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Mathematics
Mathematics
Problem
Three positive real numbers
x
,
y
,
z
x,\,y,\,z
x
,
y
,
z
are simultaneously in arithmetic progression and in geometric progression. Which of the following statements must then be true about the numbers? a)
x
:
y
:
z
=
1
:
2
:
4
x:y:z = 1:2:4
x
:
y
:
z
=
1
:
2
:
4
b)
x
:
y
:
z
=
1
:
2
:
3
x:y:z = 1:2:3
x
:
y
:
z
=
1
:
2
:
3
c)
x
=
y
=
z
x=y=z
x
=
y
=
z
d)
x
y
z
=
(
x
+
y
+
z
)
2
xyz = (x+y+z)^2
x
y
z
=
(
x
+
y
+
z
)
2
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