sequences and series - Prove that $1+{1over 1+{1over 1+{1over 1+{1over 1+...}}}}=sqrt{1+sqrt{1+sqrt{1+sqrt{1+...}}}}$

So, my professor me gave this exercise as a challenge:

-First, prove that:

$$1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}={1+\sqrt{5}\over 2}.$$

-Then, prove that:

$$1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+...}}}}$$

He said you need no advanced maths to solve it: you just need high-school math with no calculus...

The thing is that it's been 2 weeks now and I'm as lost as when I first saw the problem.

Can someone help me!