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KVPY2015MathematicsQuadratic Equation

The number of ordered pairs (x, y) of real numbers that satisfy the simultaneous equations. x+y²=x²+y=12 is

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

array l x + y ²= x ²+ y =12 x + y ²= x ²+ y x-y=x²-y² x=y, x + y =1 when x = y x ²+ x =12 x ²+ x -12=0 x ²+4 x -3 x -12=0 ( x +4)( x -3)=0 x =-4,3 (3,3)(-4,-4) When y =1- x x +(1- x )²=12 x ²- x -11=0 x= 1 1+44 2 array So four pair.

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