Let \displaystyle r=\sqrt{\frac{\sqrt{53}}{2}+\frac32}. There is a unique triple of positive integers (a,b,c) such that
r^{100}=2 r^{98}+14 r^{96}+11 r^{94}-r^{50}+a r^{46}+b r^{44}+c r^{40}
What is the value of a^2+b^2+c^2?
Answer Choices
A. 11\:421
B. 20\:229
C. 16\:291
D. 15\:339
E. 17\:115