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Think twice (Posted on 2016-09-12) Difficulty: 2 of 5
Solve for integer x:
x1/2+x1/4= 20

See The Solution Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Solution The apparent solution | Comment 1 of 4
One number is the square root of the other. Looked at the other way, the other number is the square of the first.

4^2 = 16 and 4 + 16 = 20;   x=16^2=256 , so the 4th root is 4 and the square root is 16.

But the title asks us to think twice. The only thing I can think of would be if x^(1/4) were negative and x^(1/2) were positive.  I guess it could be the other way around, if you make different choices, so that x^(1/2) is not (x^(1/4))^2, but rather -(x^(1/4))^2.

If x^(1/4) = -5 and x^(1/2) = 25 then the sum is 20; one of the 4th roots of 625 is -5 and one of the square roots is 25. So both these choices we get 25 +(-5) = 20.

Edited on September 12, 2016, 10:34 am
  Posted by Charlie on 2016-09-12 10:33:10

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