The problems are meant to be difficult, so there's nothing wrong with asking for help! In fact, it's great that you're looking at the problems early enough to have time to ask and then try to solve with a hint. That's a great way to learn!

For 7: Letting $z = b^x$ is a good start, so we get $z^2 + 3z - 1$. This is a quadratic so it's graph (max/min, where increasing, etc.) should be fairly easy to understand. One annoyance: We need to consider cases where $b > 1$ and $0 < b < 1$. Why? For example, if $b > 1$ then we know that $z=b^x$ is always increasing on the interval $[-1, 1]$, so it's max value is $z=b$ and it's minimum value is $z=b^{-1}$. What values do these give on the quadratic?

For 10: Let me try the following hint to start. Note: $$\begin{aligned} 1 + \frac{1}{1^2} + \frac{1}{2^2} &= \frac{9}{4} = \left( \frac{3}{2}\right)^2 \\ 1 + \frac{1}{2^2} + \frac{1}{3^2} &= \frac{49}{36} = \left( \frac{7}{6}\right)^2 \\ 1 + \frac{1}{3^2} + \frac{1}{4^2} &= \frac{169}{144} = \left( \frac{13}{12}\right)^2 \\ \end{aligned}$$So in general try to write $$1 + \frac{1}{k^2} + \frac{1}{(k+1)^2}$$ as a perfect square. Note this problem is very tricky!