Question
If the harmonic mean between a and b be H, then the value of 1 H -a + 1 H -b is
BITSAT
Mathematics
Sequences and Series
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. a+b
- B. a b
- C. 1 a + 1 b
- D. 1 a - 1 b
Answer
C. 1 a + 1 b
Step-by-step solution
Putting H = 2 a b a+b , we have array l 1 H -a + 1 H -b \\ = 1 ( 2 a b a+b -a ) + 1 ( 2 a b a+b -b ) = a+b a b-a^ 2 + a+b a b-b^ 2 array = ( a+b b-a ) ( 1 a - 1 b )= ( a+b b-a ) ( b-a a b )= a+b a b = 1 a + 1 b
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