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Question
If `x/a = y/b = z/c`, show that `x^3/a^3 - y^3/b^3 = z^3/c^3 = (xyz)/(zbc).`
Solution
Let `x/a = y/b = z/c = k`
x = ak, y = bk, z = ck
L.H.S.
= `x^3/a^3 - y^3/b^3 + z^3/c^3`
⇒ `(a^3k^3)/a^3 - (b^3k^3)/b^3 - (c^3k^3)/c^3`
⇒ k3 - k3 + k3= k3
R.H.S.
= `(xyz)/(abc)`
⇒ `(ak·bk·ck)/(abc)`
⇒ `(k^3abc)/(abc)`
= k3
L.H.S. = R.H.S.
Hence proved.
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