A Nice Algebra Irrational Equation | Method (2) | Geendle

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[@wes9627]

By inspection I would say that x=50i, so x and -x lie on opposite sides of a circle centered on the origin of the complex plane.
Then √x=(5√2)(√2/2)(1+i) and √(-x)=(5√2)(√2/2)(1-i) and √x+√(-x)=(5√2)(√2/2)+(5√2)(√2/2)=10.

[@Geendle]

Hi, thanks for sharing!

[@didles123]

My thinking is that √x+√(-x) = √x ± i√x = (1±i)√x => √x = 10/(1±i). No substitutions here, just brute forcing it.

[@Geendle]

Hi! Your brute force method works! Thank you!