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Question

If x=4aba+b, where ab0, then the value of x+2ax2a+x+2bx2b is
(Assume that everything is defined)

A
Independent of a
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B
Independent of b
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C
Independent of x
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D
None of these
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Solution

The correct options are
A Independent of a
B Independent of b
C Independent of x
x=4aba+bx2a=2ba+b
Applying componendo-dividendo, we get
x+2ax2a=3b+aba
Similarly x+2bx2b=3a+bab
x+2ax2a+x+2bx2b=3b+aba+3a+bab=2
So expression is independent of x, a and b
Hence, options 'A', 'B' and 'C' are correct.

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