if a b c are in g.p then proove that 1/a^2-b^2 = 1/b^2-c^2 - 1/b^2
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Answer: (b
2
−c
2
)
2
Step-by-step explanation: a,b,c are in G.P
⇒
a
b
=
b
c
⇒b
2
=ac
a
2
−b
2
1
+
b
2
1
+
b
2
−c
2
1
=
a
2
−ac
1
+
ac
1
+
ac−c
2
1
=
(a
2
−ac)(ac−c
2
)
ac−c
2
+a
2
−ac
+
ac
1
=
a(a−c)c(a−c)
−c
2
+a
2
+
ac
1
=
a(a−c)c(a−c)
(a−c)(a+c)
+
ac
1
=
ac(a−c)
(a+c)
+
ac
1
=
ac
1
[
(a−c)
(a+c)
+1]
=
ac
1
[
(a−c)
a+c+a−c
]
=
ac
1
[
(a−c)
2a
]
=
c(a−c)
2
=
(ac−c
2
)
2
=
(b
2
−c
2
)
2
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