8.1. The real number a is such that $2a - 1/a = 3$. What is the value of $16a^4 + 1/a^4$?
Answer: 161

Solution. Squaring the equality from the condition, we get $4 a^{2}-4+1 / a^{2}=9$, that is, $4 a^{2}+1 / a^{2}=13$. Squaring again, we obtain $16 a^{4}+8+1 / a^{4}=169$. Therefore, $16 a^{4}+1 / a^{4}=161$.