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प्रश्न
If a, b, c are in continued proportion and a(b – c) = 2b, prove that: `a - c = (2(a + b))/a`.
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उत्तर
Since a, b, c are in continued proportion,
`a/b = b/c`
`\implies` b2 = ac ...(i)
a(b – c) = 2b
`\implies (a(b - c))/b = 2` ...(ii)
Now,
R.H.S. = `(2(a + b))/a`
`\implies (a(b - c))/b xx (a + b)/a` ...Using equation (ii)
`\implies (cancela(b - c))/b xx (a + b)/cancela`
`\implies (b - c)/b xx a + b`
`\implies (ba + b^2 - ac - bc)/b`
`\implies (ba + ac - ac - bc)/b` ...(Using equation (I))
`\implies (ba - bc)/b`
`\implies (cancel(b)(a - c))/cancel(b)`
`\implies` a – c
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