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Question

The value of x in xbcb+c+xcac+a+xaba+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+ca
The solution in this problem can be given by back-substitution of options.
1) For option A:
LHS = a+b+cbcb+c+a+b+ccac+a+a+b+caba+b
which gives atleast one product term. So A cannot be the correct option.
2) For option B:
LHS = abcbcb+c+abccac+a+abcaba+b
which also gives product terms. So B is also not correct.
3) For option c:
LHS = ab+bc+cabcb+c+ab+bc+cacac+a+ab+bc+caaba+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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