10. Suppose $x^{2}-13 x+1=0$. What is the last digit of $x^{4}+x^{-4}$ ?
(A) 1 ;
(B) 3 ;
(C) 5 ;
(D) 7 ;
(E) 9 .
10. Ans: (D)
By assumption $x+\frac{1}{x}=13$. Thus $x^{2}+\frac{1}{x^{2}}=13^{2}-2=167$. Similarly, $x^{4}+\frac{1}{x^{4}}=167^{2}-2$, whose last digit is 7 .