Question

if a, b, c are in continued proportion -
prove that - a^2 + ab + b^2 / b^2 +bc + c^2 = a/c​

Answer 1

Answer:

a, b, c are in continued proportion

so a / b = b / c = k (say)

a= b k , b = ck

a = ck * k = c k² ,  b = ck

LHS =(a²+ ab + b²) / (b² +bc + c²)

= (c²k^4   + c²k³+ c²k²)/( c²k² + c²k + c² )

={c²k² ( k²  +  k  + 1 )} / { c² ( k²  +  k  + 1 ) }

= k²

RHS = a/c = ck²/c

= k²                                                                    

therefore LHS = RHS

HENCE PROVED

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