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Byju's Answer
Standard IX
Mathematics
Axioms
If b-c=2 ba a...
Question
If b
-
c =
2
b
a
and a
-
b = 2, then show that b
2
= ac.
Open in App
Solution
b
-
c
=
2
b
a
(
Given
)
.
.
.
(
i
)
a
-
b
=
2
(
Given
)
∴
a
-
2
=
b
.
.
.
(
ii
)
By
cross
-
multiplying
(
i
)
,
we
get
:
a
b
-
a
c
=
2
b
⇒
a
b
-
2
b
=
a
c
⇒
b
a
-
2
=
a
c
⇒
b
2
=
a
c
[
From
(
ii
)
]
Hence
proved
.
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0
Similar questions
Q.
Show that :
a
2
-
b
2
+
a
a
2
+
b
2
+
b
÷
a
2
+
b
2
-
b
a
-
a
2
-
b
2
=
b
2
d
2
Q.
If
△
1
,
△
2
be the areas of two triangles with vertices
(
b
,
c
)
,
(
c
,
a
)
,
(
a
,
b
)
, and
(
a
c
−
b
2
,
a
b
−
c
2
)
,
(
b
a
−
c
2
,
b
c
−
a
2
)
,
(
c
b
−
a
2
,
c
a
−
b
2
)
, then
△
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△
2
=
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+
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+
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)
2
Q.
Show that if A and B are square matrices such that AB = BA, then
(
A
+
B
)
2
=
A
2
+
2
A
B
+
B
2
.
Q.
Show that
∣
∣ ∣
∣
a
b
−
c
c
+
b
a
+
c
b
c
−
a
a
−
b
b
+
a
c
∣
∣ ∣
∣
=
(
a
+
b
+
c
)
(
a
2
+
b
2
+
c
2
)
Q.
If
a
,
b
,
c
and
A
,
B
,
C
∈
R
−
(
0
}
such that
a
A
+
b
B
+
c
C
+
√
(
a
2
+
b
2
+
c
2
)
(
A
2
+
B
2
+
C
2
)
=
0
, then value of
a
B
b
A
+
b
C
c
B
+
c
A
a
C
is
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