Question

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Answer 1

x^4-4=(x²-2)(x²+2)=(x-√2)(x+√2)(x²+2)

x²-(√2-1)x-√2=(x-1)(x+√2)
x1+x2=-1+√2 U x1*x2=-√2
x1=-1 U x2=+√2
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(x-√2)(x+√2)(x²+2)/(x²+2)(x+1)(x-√2)=(x+√2)/(x+1)

Answer 2

$frac{x^4-4}{(x^2+2)(x^2- (sqrt{2}-1)x- sqrt{2}) } = frac{(x^2-2)(x^2+2)}{(x^2+2)(x^2- xsqrt{2}+x- sqrt{2}) }=frac{x^2-2}{x(x+1)- sqrt{2}(x+1) }= \ = frac{(x-sqrt{2})(x+sqrt{2})}{(x- sqrt{2})(x+1) }=frac{x+sqrt{2}}{x+1 }$

Answer 3

Огромнейшее спасибо!