x^4+4x^3+3x^2+2x-1=0. Created by Unicorn1337228. algebra-ru

x^4+4x^3+3x^2+2x-1=0...

Unicorn1337228 @Unicorn1337228

August 2022 1 8 Report

x^4+4x^3+3x^2+2x-1=0

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AnonimusPro

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$x^4+4x^3+3x^2+2x-1=0
\\x^2+3x-1+x^4+4x^3+2x^2-x=0
\\x^2+3x-1+x^4+3x^3-x^2+x^3+3x^2-x=0
\\(x^2+3x-1)+x^2(x^2+3x-1)+x(x^2+3x-1)=0
\\(x^2+3x-1)(x^2+x+1)=0
\\x^2+3x-1=0
\\D=9+4=13
\\x_1= \frac{-3+\sqrt{13}}{2}
\\x_2=\frac{-3-\sqrt{13}}{2}
\\x^2+x+1=0
\\D=1-4\ \textless \ 0

$
Ответ: $x_1= \frac{-3+\sqrt{13}}{2};\ x_2=\frac{-3-\sqrt{13}}{2}$

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Unicorn1337228 August 2022 | 0 Ответы

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