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Question

# The value of x in xâˆ’bcb+c+xâˆ’cac+a+xâˆ’aba+b=a+b+c is

A
a+b+c
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B
abc
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C
ab+bc+ca
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D
a2+b2+c2
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Solution

## The correct option is C ab+bc+caThe solution in this problem can be given by back-substitution of options.1) For option A: LHS = a+b+c−bcb+c+a+b+c−cac+a+a+b+c−aba+b which gives atleast one product term. So A cannot be the correct option.2) For option B: LHS = abc−bcb+c+abc−cac+a+abc−aba+b which also gives product terms. So B is also not correct.3) For option c: LHS = ab+bc+ca−bcb+c+ab+bc+ca−cac+a+ab+bc+ca−aba+b= a(b+c)b+c+b(a+c)c+a+c(a+b)a+b= a+b+c, which is the required term in RHS.Hence, the correct option is C.

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