Предмет: Алгебра, автор: 197720022015

замена переменной. Дам 15 баллов.

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Автор ответа: ershik2001

1) х1=1, х2=-6, х3=-1, х4=-4
2) х1=1, х2=0,125
3) х1=0,5, х2=-1
Потрібно більше пояснень?

Автор ответа: Pacanka202

1) пусть а=х^2+5х
а(а–2)=24
а^2–2а–24=0
Д=/4–4•1•(–24)=/100=10
а1=(2+10)/2=6
а2=(2–10)/2=–4
х^2+5х=6
х^2+5х–6=0
х1+х2=–5
х1•х2=–6
х1=1; х2=–6
х^2+5х=–4
х^2+5х+4=0
х1+х2=–5
х1•х2=4
х1=–1; х2=–4

2) пусть (2х–1)/х=а (х не равно 0)
а–6а+5=0
–5а=–5
а=1
(2х–1)/х = 1
2х–1 = х
х=1

3) пусть (2х^2+х)=а
(а+1)(а+3)=8
а^2+3а+а+3=8
а^2+4а–5=0
а1+а2=–4
а1•а2=–5
а1=1; а2=–5
2х^2+х=1
2х^2+х–1=0
Д=/1–4•2•(-1)=/9=3
х1=(–1+3)/4=1/2
х2=(–1–3)/4=–1
2х^2+х=–5
2х^2+х+5=0
Д=/1–4•2•5<0 решений нет

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