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АлександраЯ
@АлександраЯ
July 2022
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Решите уравнение, используя введение новой переменной:
(x^2-10x)^2-3(x^2-10)-4=0
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Rechnung
Verified answer
(x²-10x)²-3(x²-10x)-4=0
t=x²-10x
t²-3t-4=0
t(1)=-1(корни найдены по т.Виета)
t(2)=4
x²-10x=-1 x²-10x=4
x²-10x+1=0 x²-10x-4=0
D=96 D=116
x1=(10+4√6)/2=
5+2√6
x3=(10-2√29)/2=
5-√29
x2=
5-2√6
x4=
5+√29
1 votes
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Answers & Comments
Verified answer
(x²-10x)²-3(x²-10x)-4=0t=x²-10x
t²-3t-4=0
t(1)=-1(корни найдены по т.Виета)
t(2)=4
x²-10x=-1 x²-10x=4
x²-10x+1=0 x²-10x-4=0
D=96 D=116
x1=(10+4√6)/2=5+2√6 x3=(10-2√29)/2=5-√29
x2=5-2√6 x4=5+√29