(x^2-2x)^2-(x-1)^2+1=0 Найдите корни. Created by safna0411. algebra-ru

(x^2-2x)^2-(x-1)^2+1=0 Найдите корни...

June 2022 1 11 Report

(x^2-2x)^2-(x-1)^2+1=0
Найдите корни

Answers & Comments

krugly1981 X⁴ - 4x³ + 4x² - ( x² - 2x + 1) + 1 = 0
x⁴ - 4x³ + 4x² - x² + 2x - 1 + 1 =0
x⁴ - 4x³ + 3x² + 2x= 0
Разложим на множители и решим:
x( x - 2)(x² - 2x - 1) =0
Произведение равно 0,когда один из множителей равен 0,значит,
x = 0
x- 2 = 0
x = 2
x² - 2x - 1 = 0
D = b² - 4ac = 4 - 4×(-1) = 8
x1 = ( 2 + 2√2)/2 = 2( 1 + √2)/2 = 1 + √2
x2 = ( 2 - 2√2)/ 2 = 2( 1 - √2)/2 = 1 - √2

Ответ: x1 = 1 + √2, x2 = 1 - √2, x3 = 0, x4 = 2.

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