Let \(a,b,c,\) and \(d\) be distinct real numbers such that

\(\begin{align*} a &= \sqrt{4 + \sqrt{5 + a}}, \\ b &= \sqrt{4 - \sqrt{5 + b}}, \\ c &= \sqrt{4 + \sqrt{5 - c}}, \\ d &= \sqrt{4 - \sqrt{5 - d}}. \end{align*}\)

Compute \(abcd.\)

Guest Sep 1, 2020

#3**+3 **

For anyone who can't seem to see the LaTeX, here is the picture:

(I plugged it into a latex site and screenshoted it)

But I'm not just here to give you a picture of something you probably already know.

After quite a long time of confusion, I finally got the answer! I actually first searched this question just to make sure that it wasn't answered before. And I found this link. Guest's answer confused me, because he/she said there was no answer. So I decided to try myself, and I got an answer to an "unanswerable" question.

Let the variable 'x' represent a, b, c and d.

We can say this:

Square both sides:

Subtract 4:

Square again!

Multiply out the left side:

Subtract 5:

We could keep on going, but remeber, we want abcd, not the equation for it. Using vieta's formula, we see that abcd = 11/1 = **11**

**That is the answer to your "unanswerable" question **

**:)**

ilorty Sep 1, 2020