If a, b, c and d are in proportion, prove that: (a+c)3(b+d)3=a(a-c)2b(b-d)2

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)`

Sum

∵ 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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Chapter 6: Ratio and Proportion - Exercise 7.2

Chapter 6 Ratio and Proportion
Exercise 7.2 | Q 19.5

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