Finding dot product from $|a|, \ |b|, \ |a+b|$

Question

For vectors $a,b$ we know that $|a|=2$, $|b|=3$ and $|a+b|=4$. I want to find the dot product $a\cdot b$.

Any ideas?

Answer 1

$$|a+b|^2=(a+b)^2=a^2+2\,a\cdot b+b^2=|a|^2+2\,a\cdot b+|b^2|.$$