If x and y are positive integers such that  xy+x+y = 71,  x2y +xy2 =880, then x 2+y2 is equal to

If x and y are positive integers such that  xy+x+y = 71,  x2y +xy2 =880, then x 2+y2 is equal to

  1. A
  2. B
  3. C
  4. D

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    Solution:

    xy+x+y=71xy+(x+y)=71

    and  x2y+xy2=880 xy(x+y)=880

    xy and (x+y) are the roots of the quadratic equation. 

    t271t+880=0(t55)(t16)=0t=55,16x+y=16andxy=55

    So,x2+y2=(x+y)22xy=(16)2110=146

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