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Byju's Answer
Standard X
Mathematics
Invertendo
If a, b, c ...
Question
If
a
,
b
,
c
are in A.P. then prove that
1
b
c
,
1
c
a
,
1
a
b
are also in A.P
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Solution
It is given that
a
,
b
,
c
are in A.P.
Divide each term by
a
b
c
, so we get,
a
a
b
c
,
b
a
b
c
,
c
a
b
c
are also in A.P
Now by simplifying we get,
1
b
c
,
1
a
c
,
1
a
b
are in A.P
Hence proved.
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Similar questions
Q.
If
1
a
,
1
b
,
1
c
are in A.P., prove that
(i)
bc,ca,ab are in A.P.
(ii) a(b+c), b(c+a), c(a+b) are in A.P
Q.
1
a
,
1
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and
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Q.
If 1/a, 1/b, 1/c, are in a.p prove that BC, ca, an are in a.p
hints: prove that ab- ca =ca- BC
Using 1/c - 1/b = 1/b - 1/a.
Q.
If a, b, c are in A.P., then the following are also in A.P.
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Q.
If
b
+
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a
,
c
+
a
b
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+
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are in A.P., prove that:
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are in A.P.
(ii) bc, ca, ab are in A.P.
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