The solution set of the inequation $3^x+3^{1-x}-4 < 0$ is

The set of values of $x$ for which the inequalities $x^2-3x-10 < 0$ and $10x-x^2-16 > 0$ hold simultaneously is:

Let $f(x) = x^2 + 4x + 1$. Then

Let $\alpha$ and $\beta$ be the distinct roots of the equation $x^2 - (t^2 - 5t + 6)x + 1 = 0$,where $t \in \mathbb{R}$,and $a_n = \alpha^n + \beta^n$. Then the minimum value of $\frac{a_{2023} + a_{2025}}{a_{2024}}$ is

If the inequality $kx^2 - 2x + k \geq 0$ holds good for at least one real $x$,then the complete set of values of $k$ is

The integer $k$,for which the inequality $x^{2}-2(3k-1)x+8k^{2}-7>0$ is valid for every $x \in \mathbb{R}$,is