(х^2-2х-1)^2+3(х-1)^2=16. Created by sokky. algebra-ru

(х^2-2х-1)^2+3(х-1)^2=16...

sokky @sokky

July 2022 1 8 Report

(х^2-2х-1)^2+3(х-1)^2=16

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sangers1959

Verified answer

(x²-2x-1)²+3(x-1)²=16
((x²-1)-2x)²+3(x-1)²=16
(x²-1)²-4x(x²-1)+4x²+3x²-6x+3=16
x⁴-2x²+1-4x³+4x+4x²+3x²-6x+3=16
x⁴-4x³+5x²-2x-12=0
x₁=-1
x⁴-4x³+5x²-2x-12 |_x+1_
x⁴+x³ | x³-5x²+10x-12
--------
-5x³+5x²
-5x³-5x²
------------
10x²-2x
10x²+10x
-------------
-12x-12
-12x-12
-----------
0
x³-5x²+10x-12=0
x₂=3
x³-5x²+10x-12 |_x-3_
x³-3x² | x²-2x+4
--------
-2x²+10x
-2x²+6x
-------------
4x-12
4x-12
---------
0
x²-2x+4=0 D=-12 ⇒ Уравнение не имеет действительных корней.
Ответ: x₁=-1 x₂=3.

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sokky November 2021 | 0 Ответы

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