Решите уравнение: [tex]2-3x+x^2=2(x-1)* \sqrt{x} [/tex]. Created by НоВыЙ13. algebra-ru

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Решите уравнение:
[tex]2-3x+x^2=2(x-1)* \sqrt{x} [/tex]

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sedinalana

Verified answer

ОДЗ
x∈[0;∞)
x²-3x+2=(x-2)(x-1)
x1+x2=3 U x1*x2=2⇒x=1 U x=2
(x-1)(x-2)-2(x-1)√x)=0
(x-1)(x-2-2√x)=0
x-1=0
x=1
x-2√x-2=0
√x=a
a²-2a-2=0
D=4+8=12
a1=(2-2√3)/2=1-√3⇒√x=1-√3<0 нет решения
a2=1+√3⇒√x=1+√3⇒x=(1+√3)²=4+2√3

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