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Question
Find the third proportional to a – b and a2 – b2
Solution
Let the third proportional to a – b and a2 – b2 be x.
`=>` a – b, a2 – b2, x are in continued proportion.
`=>` a – b : a2 – b2 = a2 – b2 : x
`=> (a - b)/(a^2 - b^2) = (a^2 - b^2)/x`
`=> x = (a^2 - b^2)^2/(a - b)`
`=> x = ((a + b)(a - b)(a^2 - b^2))/(a - b)`
`=>` x = (a + b)(a2 – b2)
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