a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find a+b+c=?
Pick one: A) 13 B) 14 C) 15 D) 16 E) 17
a^2*b^2+a^2+b^2+1= (a^2+1)(b^2+1)   by using above one we can write   a^2*b^2+a^2+b^2+1=260..(1)   b^2*c^2+b^2+c^2+1=1300..(2)   c^2*a^2+c^2+a^2+1=500..(3)   by doing (1)/(2) we will get a^2+1/c^2+1 = 1/5..(4)   by doing (4)*(3) we will get (a^2+1)^2=10,   by solving a=3, b=5,c=7   so a+b+c=15   ANSWER:15
<result>C</result>
a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find a+b+c=?