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

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

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.

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

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.