## (x^a+b)^2 (x^b+c)^2 (x^c+a)^2/( x^a*x^b*x^c)^4​

Question

(x^a+b)^2 (x^b+c)^2 (x^c+a)^2/( x^a*x^b*x^c)^4​

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10 hours 2021-11-25T09:18:56+00:00 1 Answer 0 views 0

1. Step-by-step explanation:

in above equation, to convert the denominator in terms variable in numerator only, substitute, a+b+c=y

So, above equation becomes,

x−a2y−a+x−b2y−b+x−c2y−c=4y

Just for a the sake of cancelling the denominator terms, substitute x=y2 in this, so we get

y2−a2y−a+y2−b2y−b+y2−c2y−c=4y

(y−a)(y+a)(y−a)+(y−b)(y+b)(y−b)+(y−c)(y+c)(y−c)=4y

(y+a)+(y+b)+(y+c)=4y

3y+a+b+c=4y i.e. y=a+b+c

So, this is the same value as per our assumption which is indeed found to be true.

Hence, x=y2 i.e. x=(a+b+c)2 is the solution of above equation.