已知a+b=4n+2,ab=1,若19a2+150ab+19b2的值为2012,则n=
问题描述：
已知a+b=4n+2,ab=1,若19a2+150ab+19b2的值为2012,则n=
答
19a^2+150ab+19b^2
=19a^2+38ab+19a^2+112ab
=19(a+b)^2+112ab
=19(4n+2)^2+112=2012
则19(4n+2)^2=1900
(4n+2)^2=100
4n+2=10或-10
n=2或n=-3