If 2(y-a) is HM between y-x and y-z then x-a, y-a, I-a are inApHpGpNone
Anvita Mahajan , 5 Years ago
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Algebra> If 2(y-a) is HM between y-x and y-z then ...
1 AnswersSamyak Jain
Last Activity: 5 Years ago
2(y – a) is HM between y – x and y – z. 
y – x , 2(y – a) , y – z are in HP.
i.e. 1 / (y – x) , 1 / 2(y – a) , 1 / (y – z) are in AP.
1 / (y – a) = 1 / (y – x) + 1 / (y – z) 1 / (y – a) – 1 / (y – x) = 1 / (y – z)
(y – x – y + a) / (y – a)(y – x) = 1 / (y – z)
– (x – a) / (y – a)(y – x) = 1 / (y – z) 
(x – a) / (y – x) = (y – a) / (z – y)
(x – a) / [(y – a) – (x – a)] = (y – a) / [(z – a) – (y – a)]
By invertendo, [(y – a) – (x – a)] / (x – a) = [(z – a) – (y – a)] / (y – a)
i.e. {(y – a) / (x – a)} – 1 = {(z – a) / (y – a)} – 1 (y – a) / (x – a) = (z – a) / (y – a)
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