Let a, b, c, and d be distinct real numbers such that a = sqrt{4 + sqrt{5 + a}}, b &= sqrt{4 - sqrt{5 + b}}, c = sqrt{4 + sqrt{5 - c}}, d = sqrt{4 - sqrt{5 - d}}. Compute abcd.
The solutions are 2.2192, 1.33938, 1.09044, and 2.4682, and their product is 8.
I don't know how to do these algebraicly, so I graphed them. These are the answers that I got:
a = 2.599364238
b = 1.226651563
c = 2.370956068
d = 1.455059732
Their product is 11.
