Question

if a b c are in HP where a b + BC + CA = 15 then the value of CA equals to​

Answer 1

value of ac comes out as 5

Answer 2

Answer:

Step-by-step explanation:

Since a,b,c are in harmonic progression, their  

reciprocals 1%2Fa,1%2Fb,1%2Fc form an arithmetic sequence:

Let d be the common difference.  Then

1%2Fa%2Bd%22%22%2B%22%221%2Fb

1%2Fb%2Bd%22%22%2B%22%221%2Fc

Solve each for d

d%22%22=%22%221%2Fb-1%2Fa

d%22%22=%22%221%2Fc-1%2Fb

Since both equal d, they are equal to each other:

1%2Fb-1%2Fa%22%22=%22%221%2Fc-1%2Fb

Multiply through by LCD of abc

ac - bc = ab - ac

2ac = ab + bc

And since we are given that

ab + bc + ca = 15

We can substitute 2ac for ab + bc and get

2ac + ca = 15

And since ac is the same as ca

2ca + ca = 15

3ca = 15

ca = 5