If x varies y and y varies z then prove that, x3 + +z3 varies 3xyz.
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Given x+y+z=0. ⟹x+y=−z. Cubing on both sides. (x+y)3=(−z)3. ⟹x3+y3+3x2y+3xy2=−z3. ⟹x3+y3+3xy(x+y)=−z3. ⟹x3+y3+3xy(−z)=−z3. ⟹x3+y3−3xyz=−z3.
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