I was wondering which branch / part of mathematics deals with inequalities & questions like the ones I've linked, and if there are any books or lectures that surround the topic. I've tried looking for an answer but I can't really find anything which satisfies what I'm looking for.
question 1:
Given $a\geq 0$ , find all solutions for $a$.
$x^2+|x-a| - |x+a| = 0$
question 2:
solve the following equation.
$\sqrt{x+\sqrt{x²-1}} = 2 - \sqrt x$
I was able to solve this one but it took me like 25 minutes to figure out.
If you need more info ask away and I'll try to find more examples / answer your questions, thanks!