(x-a/b+c)+(x-b/c+a)+(x-c/a+b)=3 find the value of x
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Method 1 :
(x-a)(a+b)(a+c)+(x-b)(b+c)(b+a)+(x-c)(c+a)(c+b) = 3(a+b)(b+c)(c+a)
Scary as it looks, expand it and solve to get x = a+b+c
Method 2 :
Subtract 1 from each of the clubbed terms from the lhs. The rhs can be used to et the three 1s required for this. You will get x-a-b-c as one factor multiplied by some other factor equal to zero. Assuming the other factor to be non zero, you get x = a+b+c.
(x-a)(a+b)(a+c)+(x-b)(b+c)(b+a)+(x-c)(c+a)(c+b) = 3(a+b)(b+c)(c+a)
Scary as it looks, expand it and solve to get x = a+b+c
Method 2 :
Subtract 1 from each of the clubbed terms from the lhs. The rhs can be used to et the three 1s required for this. You will get x-a-b-c as one factor multiplied by some other factor equal to zero. Assuming the other factor to be non zero, you get x = a+b+c.
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