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Question
If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^2/b^2 + z^3/c^2 = ((x + y + z)^3)/((a + b ++ c)^2)`.
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Solution
Let `x/a = y/b = z/c = k` ...[By k method]
x = ak, y = bk and z = ck.
L.H.S.
= `(a^3k^3)/(a^2) + (b^3k^3)/(b^2) + (c^3k^3)/(c^2)`
⇒ k3 [a + b + c]
R.H.S.
= `[ak + bk + ck]^3/[a + b + c]^2`
⇒ `(k^3[a + b + c]^3)/[a + b + c]^2`
= k3 (a + b + c)
L.H.S. = R.H.S.
Hence proved.
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