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प्रश्न
If (p – x) : (q – x) be the duplicate ratio of p : q then show that : `1/p + 1/q = 1/x`.
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उत्तर
We have,
`(p -x)/(q - x) = p^2/q^2`
`=>` q2(p – x) = p2(q – x)
`=>` pq2 – q2x = p2q – p2x
`=>` p2x – q2x = p2q – pq2
`=>` x(p2 – q2) = pq(p – q)
`=>` x(p – q)(p + q) = pq(p – q)
`=> x = (pq)/(p + q)`
`=> (p + q)/(pq) = 1/x`
`=> p/(pq) + q/(pq) = 1/x`
`=> 1/p + 1/q = 1/x`
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