Q:

What is the mathematical mystery here?

I know that, $$\sqrt{25}=5≠-5$$
But, in quadratic equation we write $$(2ax+b)^2=b^2-4ac$$

$$(2ax+b)=±\sqrt{b^2-4ac}$$

Why?? We must write $±$, and What is the mathematical mystery here?

A:

In $\mathbb{R}$ there are two numbers $x$ such that $x^2=a$ (for $a>0$), and these two numbers have opposite sign, but, by definition, the symbol $\sqrt{a}$ indicates only the positive one of such two numbers, so, if we want indicate expliciltly all the two we must write $ x= \pm \sqrt{a}$.

