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प्रश्न
If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.
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उत्तर
b is the mean proportional of a and c
b2 = ac
b2 = `((b + c)/(2)). ((a + b)/(2))`
⇒ 4b2 = ab + ac + b2 + bc ...[∵ b2 = ac]
⇒ 4b2 = ab + 2b2 + bc
2b2 - ab + bc,
`["Dividing both sides by abc"]`
⇒ `(2b^2)/(abc) = (ab)/(abc) + (bc)/(abc)`
⇒ `(2)/b = (1)/c + (1)/a`, ...[∵ b2 = ac]
Hence proved.
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