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Let x/a = y/b = z/c = k
x = ak, y = bk, z = ck
L.H.S. = x3/a3 – y3/b3 + z3/c3 ⇒ a3k3/a3 – b3k3/b3 – c3k3/c3
⇒ k3 – k3 + k3 = k3
R.H.S. = xyz/abc ⇒ ak.bk.ck/abc ⇒ k3abc/abc = k3
L.H.S. = R.H.S.
Hence proved.
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