Question 89
a) Find all values of $a$ for which the inequality
$$
x \log_{\frac{1}{2}} a^4 - x^2 \gt 3 + 2 \log_2 a^2
$$
has a solution.
b) Calculate the limit
$$
\lim_{a \to -\infty} \left( \sqrt{a^2 - a + 1} + a \right).
$$
$$
x \log_{\frac{1}{2}} a^4 - x^2 \gt 3 + 2 \log_2 a^2
$$
has a solution.
b) Calculate the limit
$$
\lim_{a \to -\infty} \left( \sqrt{a^2 - a + 1} + a \right).
$$