Question

If a,b,c are i. HP prove that bc/b+c,ca/c+a,ab/a+b are in hp

Answer 1

Answer:

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

Step-by-step explanation:

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