Sweden | A Nice Algebra Problem

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[hansvanderwerf]

Am i missing something?
Why bother with substitution?

sqrt(x+3) + sqrt(-x-3) = 4
sqrt(x+3) + i * sqrt(x+3) = 4
sqrt(x+3) * (1 + i) = 4
sqrt(x+3) = 4 /(1+i)
sqrt(x+3) = (4/(1+i)) * ((1-i)/(1-i)) = 2 - 2i
x+3 = ± sqr(2-2i) = ± (-8i)
x= -3 ± 8i

[Andrey-M-vtwpfgk]

38 лет после окончания университета проработал инженером-конструктором и программистом, ни разу не применял мнимую единицу

[techwithsingh]

Why did I get only one value of x
√x+3 + √x+3 i = 4
X+3 - (x+3) + 2 (x+3) i =16
X+3 =8/i
X=8/i-3
X=(8-3i)/i
X=(8i+3)/-1
X=-3-8i

[arnoldvanhofwegen]

square root of t and square root of negative t. one of them not defined so useless unless imaginary solution required.