x + y^2 = 13 y + x^2 = 13 x and y are integers then x.y will be

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14 Aug 2012 solve

x + y^2 = 13
y + x^2 = 13
x and y are integers
then x.y will be

OPtion

1) -6
2) -8
3) -10
4) -12
5) -14
6) -15
7) -18
8) -20
9) -21
10) none of these

Solution

on subtracting the two equations we get
(x-y)-(x^2-y^2)= 0
or (x-y)[1-(x+y)] = 0
so x=y or x+y=1
x=y will not provide integral solution so x+y = 1
now add the equations we get (x+y)+(x^2+y^2)=26
so (x+y)+[(x+y)^2-2x.y]=26
or 1+[1-2x.y]=26
or 2-2x.y = 26
or 2x.y = -24
or x.y = -12

Correct Option: 4 Best Solution (0)