abc(a +b+c)/³(bc + ca + ab)³ = 1
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Answer:
Answer:−
a,b,c are a continued proportion
=> b = ak
& c = bk = (ak)k = ak²
LHS
= abc(a + b + c)³
= a(ak)(ak²)(a + ak + ak²)³
= a³k³ a³(1 + k + k²)³
= a⁶k³(1 + k + k²)³
RHS
= (ab + bc + ca)³
= (aak + akak² + ak²a)³
= (a²k + a²k³ + a²k)³
= (a²k(1 + k² + k))³
= (a²k)³(1 + k + k²)³
= a⁶k³(1 + k + k²)³
LHS = RHS
QED
Proved
abc(a + b + c)³ = (ab + bc + ca)³
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