insert two numbers between 1/4 and 1/3 so that the resulting sequence is a H.P
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HELLO MATE.
1/4 , a , b , 1/13 are in HP
=> a = (2(1/4)b ) /(1/4 + b)
=> a = 2b/(4b + 1)
=> 4ab + a = 2b Eq1
b = (2(1/13)a ) /(1/13 + a)
=> b = 2a /(13a + 1))
=> 13ab + b = 2a Eq2
4*Eq2 - 13 * eq1
=> 4b - 13a = 8a - 26b
=> 30b = 21a
=> 10b = 7a
4ab + a = 2b
=> 4a (7a/10) + a = 2(7a/10)
=> 28a² + 10a = 14a
=> 28a² = 4a
=> a = 1/7
10b = 7a
=> 10b = 1
=> b = 1/10
so 1/7 & 1/10 to be inserted.
Hope it helps you mate.
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@ ANUSHA ❤✌
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