Proof Problems on Proportion

Question

If $ a/b=b/c $ then prove that $a^2b^2c^2[1/a^3 + 1/(b^3+c^3)]=a^3+b^3+c^3$

I tried by assuming $a/b=b/c=k$ but disld not get LHS=RHS

Answer 1

HINT: we have $$a^2b^2c^2(1/a^2+1/b^2+1/c^2)-(a^3+b^3+c^3)=-{\frac { \left( {a}^{2}-bc \right) \left( ab-{c}^{2} \right) \left( ac-{b}^{2} \right) }{abc}} $$