решите уравнение х^3-4х^2-х+4=0 должно быть 3 ответа. Created by JOKE367. algebra-ru

решите уравнение х^3-4х^2-х+4=0 должно быть 3 ответа...

JOKE367 @JOKE367

August 2022 2 4 Report

решите уравнение
х^3-4х^2-х+4=0
должно быть 3 ответа

maymr

Verified answer

x³ - 4x² - x + 4 = 0

x³ - x - 4x² + 4 = 0

x(x² - 1) - 4(x² - 1) = 0

(x² - 1)(x - 4) = 0

x² - 1 = 0 или x - 4 = 0

x² = 1 x = 4

x = ±1

Ответ: -1; 1; 4

2 votes Thanks 1

lilyatomach

Verified answer

Ответ:

-1; 1; 4.

Объяснение:

$x^{3} -4x^{2} -x+4=0;\\(x^{3} -4x^{2} )- (x-4)=0;\\x^{2} (x-4)-(x-4)=0;\\(x-4) (x^{2} -1)=0;\\(x-4)(x-1)(x+1)=0;\\\left [\begin{array}{lcl} { {x -4= 0,} \\ {x-1=0,} \\ {x+1= 0;} }\end{array} \right.\Leftrightarrow\left [\begin{array}{lcl} { {x = 4,} \\ {x=1,} \\ {x = -1.} }\end{array} \right.$

1 votes Thanks 1

Answers & Comments

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