Question

3. If a, b, c are in continued proportion, prove that:
(i)) (a + b + c) (a - b + c) = a^2 + b^2 + c^2
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Answer 1

Answer:

check this,

if a, b,c are in continued proportion,

then a = a, b = ar and c = ar^2 , where r is common ratio

LHS,

(a+b+c)(a-b+c) = a^2(1+r+r^2)(1-r+r^2) = a^2(1+r+r^2 -r -r^2 -r^3 +r^2 +r^3 +r^4 ) = a^2(1+r^2 +r^4 )

RHS,

(a^2+b^2+c^2) = a^2(1+r^2+r^4)

It is proved that LHS = RHS, hence (a+b+c)(a-b+c) = (a^2+b^2+c^2)

I hope this helps you.

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