Question

ONLY FOR MATHS ARYABHATTA,GENIUS AND UPPER RANKERS

If a,b,c are in A.P . Prove that the following is in A.P with the most suitable method

${a}^{2} (b + c). {b}^{2} (c + a). {c}^{2} (a + b) \: is \: in \: a.p$
That dot(.) is comma(,)


PLEASE NO SPAMMING
NEED URGENT

Answer 1

Hey there,

There are various methods for solving this.

METHOD--1

IF a,b,c are in AP

=>a/abc , b/abc ,c/abc are also in AP

=>1/bc ,1/ac. ,1/ab. Are in AP

=>(ab+bc+ca)/bc ,(ab+bc+ca)/ac ,

(ab+bc+ca)/ab are also in AP

=>1+(ab+ca)/bc ,1+(ab+bc)/ac,

1+(bc+ca)/ab are also in AP.

=>(ab+ca)/bc ,(ab+bc)/ac ,(bc+ca)/ab

are also in AP.

=>a(b+c)/bc ,b(a+c)/ac, c(a+b)/ab are

also in AP.

=>a^2(b+c),b^2(a+c),c^2(a+b) are also

in AP[multiplying by abc]

Hope it helps.