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KEAM 2017 Math Paper
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© examsnet.com
Question : 87
Total: 120
Three numbers x, y, and z are in arithmetic progression. If
x
+
y
+
z
=
–
3
and
x
y
z
=
8
,
then
x
2
+
y
2
+
z
2
is equal to
9
10
21
20
1
Validate
Solution:
Let
x
=
a
−
r
,
y
=
a
,
z
=
a
+
r
Now, we have
x
+
y
+
z
=
−
3
∴
a
−
r
+
a
+
a
+
r
=
−
3
⇒
3
a
=
−
3
⇒
a
=
−
1
Again,
x
y
z
=
8
∴
(
a
−
r
)
(
a
)
(
a
+
r
)
=
8
⇒
a
(
a
2
−
r
2
)
=
8
⇒
−
1
(
1
−
r
2
)
=
8
⇒
−
1
+
r
2
=
8
⇒
r
2
=
9
⇒
r
=
±
3
∴
x
,
y
,
z
are -4,-1,2 or 2,-1,-4
∴
x
2
+
y
2
+
z
=
(
−
4
)
4
+
(
−
1
)
2
+
(
2
)
2
=
16
+
1
+
4
=
21
© examsnet.com
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