Question

If a,b,c are in continued proportion, show that :a^2+b^2/b(a+c)=b(a+c)/b^2+c^2

Answer 1

Answer:

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)