If a,b,c are in hp then 1/b-a + 1/b-c is equal to
Answers
Given : a , b , c are in HP
To Find : 1/(b - a) + 1/(b - c)
Solution:
a , b , c are in HP
=> 2/b = 1/a + 1/c
=> 2/b = (a + c)/ac
= b = 2ac/(a + c)
1/(b - a) + 1/(b - c)
substitute b = 2ac/(a + c)
= 1/(2ac/(a + c) - a) + 1/(2ac/(a + c) - c)
= (a + c) /(2ac - a² - ac) +(a + c)/(2ac - ac - c²)}
= (a + c) /( ac - a² ) + (a + c)/( ac - c²)}
= (a + c)/a( c - a ) - (a + c)/c( c - a)
= {(a + c)/( c - a) } ( 1/a - 1/c)
= {(a + c)/( c - a) } (c - a)/ac
=(a + c)/ac
=1/c + 1/a
= 1/a + 1/c
1/(b - a) + 1/(b - c) = 1/a + 1/c
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Answer:- 2/b
See the explanation in the attachment
