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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 = sqrt4 + sqrt(5-c))

d = sqrt4 - sqrt(5-d))
Compute abcd.

 May 28, 2020
 #1
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The solutions are 2.2192, 1.33938, 1.09044, and 2.4682, and their product is 8.

 May 31, 2020

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