2.122 Given real numbers $a, b$ satisfy $\frac{4}{a^{4}}-\frac{2}{a^{2}}-3=0$ and $b^{4}+b^{2}-3=0$. Then the value of the algebraic expression $\frac{a^{4} b^{4}+4}{a^{4}}$ is 
(A) 175
(B) 55 .
(C) 13 .
(D) 7 .
(China Beijing Junior High School Mathematics Competition, 1990)
[Solution] From the given, we know $\left(\frac{2}{a^{2}}\right)^{2}-\left(\frac{2}{a^{2}}\right)-3=0$, then $\frac{2}{a^{2}}=\frac{1+\sqrt{13}}{2}$ (negative value discarded).
Similarly, $b^{2}=\frac{-1+\sqrt{13}}{2}$ (negative value discarded). $\therefore \quad \frac{a^{4} b^{4}+4}{a^{4}}=b^{4}+\frac{4}{a^{4}}=\left(3-b^{2}\right)+\left(\frac{2}{a^{2}}+3\right)=7$. Therefore, the answer is $(D)$.