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Question

The number of pairs (x,y) where both x and y are real satisfying x2 + y2 + 2 = ( 1+x )(1 + y) is


A

0

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B

1

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C

3

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D

4

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Solution

The correct option is B

1


1.Given x2 + y2 + 2 = 1 + x + y + xy. Mutiplying both sides by 2 and rewriting, we get

(x - y)2 + (x - 1)2 + (y - 1)2 = 0. As x, y are real, this implies x - y = 0, x - 1 = 0 and y - 1 = 0

i.e., x = y = 1 is the unique solution.

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