If a,b,c are in continued proportion, show that :a^2+b^2/b(a+c)=b(a+c)/b^2+c^2
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Step-by-step explanation:
if a, b,c are in continued proportion, then a = a, b = ar and c = ar2 , where r is common ratio
LHS = (a+b+c)(a-b+c) = a2(1+r+r2)(1-r+r2) = a2(1+r+r2 -r -r2 -r3 +r2 +r3 +r4 ) = a2(1+r2 +r4 )
RHS = (a2+b2+c2) = a2(1+r2+r4)
It is proved that LHS = RHS, hence (a+b+c)(a-b+c) = (a2+b2+c2)
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