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KVPY2010MathematicsBinomial Theorem

Suppose m , n are positive integers such that 6^ m +2^ m + n 3^ w +2^ n =332 . The value of the expression m ²+ mn + n ² is-

Options

  1. A7
  2. B13
  3. C19
  4. D21

Correct answer

C. 19

Step-by-step solution

6^ m +2^ m + n 3^ w +2^ n =332 maximum possible value of m is 3 checking for m =3,2 and 1 we get m =2, n =3, w =2 m ²+ mn + n ²=4+6+9=19

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