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Mathematics
If a, b, c, d and e are positive real numbers such that a+b+c+d+e=15 and a b2 c3 d4 e5=(120)3(50), then the value of a2+b2+c2+d2+e2 is ldots ldots ldots
Q. If
a
,
b
,
c
,
d
and
e
are positive real numbers such that
a
+
b
+
c
+
d
+
e
=
15
and
a
b
2
c
3
d
4
e
5
=
(
120
)
3
(
50
)
, then the value of
a
2
+
b
2
+
c
2
+
d
2
+
e
2
is
………
444
174
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NTA Abhyas 2022
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Answer:
55
Solution:
We have given that,
a
+
b
+
c
+
d
+
e
=
15
A
M
=
15
[
a
+
2
b
+
2
b
+
3
c
+
3
c
+
3
c
+
4
d
+
4
d
+
4
d
+
4
d
+
5
e
+
5
e
+
5
e
+
5
e
+
5
e
]
A
M
=
1
GM
=
(
a
⋅
2
2
b
2
⋅
3
3
c
3
⋅
4
4
d
4
⋅
5
5
e
5
)
15
1
GM
=
2
2
⋅
3
3
⋅
4
4
⋅
5
5
(
120
)
3
⋅
50
=
1
GM
=
1
∴
A
M
=
GM
Hence,
a
=
2
b
=
3
c
=
4
d
=
5
e
∴
a
2
+
b
2
+
c
2
+
d
2
+
e
2
=
1
2
+
2
2
+
3
2
+
4
2
+
5
2
=
6
5
×
6
×
11
=
55