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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.

 Jan 27, 2020
 #1
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The solutions are 2.2192, 1.33938, 1.09044, and 2.4682, and their product is 8.

 Jan 27, 2020
 #2
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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.

 Jan 27, 2020

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