Question

A/b=b/c prove that (a+b+c) (a2+b2+c2)

Answer 1

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Topperlearning ICSE Class 10 - Ask The Expert Answered

If a,b,c are in continued proportion prove that: ( a+b+c)(a-b+c)=a2 +b2+c2

Asked by munnamgautam20 | 25th Jan, 2019,  10:29: PM

Expert Answer:

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)