if a, b, c are in H.P. prove that b+a/b-a+b+c/b-c
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Step-by-step explanation:
a,b,c are in H.P
⇒
a
1
,
b
1
,
c
1
areinA.P
⇒
a
1
+
c
1
=
b
2
⇒a+c=
b
2ac
⇒ab+bc=2ac
Now,
b−a
b+a
+
b−c
b+c
=
(b−a)(b−c)
(b+a)(b−c)+(b+c)(b−a)
=
b
2
−ab+ac−bc
b
2
+ab−bc−ac+b
2
−ab+bc−ab
=
b
2
−2ac+ac
2b
2
−2ac
=
b
2
−ac
2(b
2
−ac)
=2
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