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KVPY2011MathematicsStraight Lines

The maximum possible value of x²+y²-4 x-6 y, x, y real, subject to the condition |x+y|+|x-y|=4

Options

  1. Ais 12
  2. Bis 28
  3. Cis 72
  4. Ddoes not exist

Correct answer

B. is 28

Step-by-step solution

|x+y|+|x-y|=4 represent a square x²+y²-4 x-6 y=(x-2)²+(y-3)²-13= (distance point on square from (2,3))²-13 Maximum =(-2-2)²+(-2-3)²-13=28

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