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Byju's Answer
Standard VI
Mathematics
Continued or Mean Proportion
If a, b, c ...
Question
If
a
,
b
,
c
are in continued proportion, prove that
(
a
+
b
+
c
)
(
a
−
b
+
c
)
=
a
2
+
b
2
+
c
2
Open in App
Solution
To Prove :
(
a
+
b
+
c
)
(
a
−
b
+
c
)
=
a
2
+
b
2
+
c
2
Proof :
a
,
b
,
c
are in continued proportion.
∴
a
b
=
b
c
=
k
(let)
b
=
c
k
a
=
b
k
=
(
c
k
)
k
=
c
k
2
L.H.S.
=
(
c
k
2
+
c
k
+
c
)
(
c
k
2
−
c
k
+
c
)
=
c
2
(
k
2
+
k
+
1
)
(
k
2
−
k
+
1
)
=
c
2
[
(
k
2
+
1
)
2
−
(
k
)
2
]
=
c
2
[
k
4
+
2
k
2
+
1
−
k
2
]
=
c
2
[
k
4
+
k
2
+
1
]
R.H.S.
=
c
2
k
4
+
c
2
k
2
+
c
2
=
c
2
[
k
4
+
k
2
+
1
]
L.H.S
=
R.H.S.
Suggest Corrections
3
Similar questions
Q.
If a, b, c, d are in continued proportion, prove that:
(
b
−
c
)
2
+
(
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2
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=
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Q.
If (a + b + c) (a
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show that a, b, c are in continued proportion.
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If (a + b + c) (a
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. then show that a, b, c are in continued proportion.
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If
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,
b
,
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,
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√
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+
c
2
:
√
b
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=
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c
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√
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Q.
If
a
,
b
,
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are in continued proportion prove that:
(i)
a
2
+
a
b
+
b
2
b
2
+
b
c
+
c
2
=
a
c
(ii)
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2
+
b
2
+
c
2
(
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+
b
+
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Continued or Mean Proportion
Standard VI Mathematics
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