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Question
If a, b, c and d are in proportion, prove that: `(a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)`
Solution
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
L.H.S. = `(a + c)^3/(b + d)^3`
= `(bk + dk)^3/(b + d)^3`
= `(k^3(b + d)^3)/(b + d)^2`
= k3
R.H.S. = `(a(a - c)^2)/(b(b - d)^2`
= `(bk(bk - dk)^2)/(b(b - d)^2`
= `(bk.k^2(b - d)^2)/(b(b - d)^2`
= k3
∴ L.H.S. = R.H.S.
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