Предмет: Математика, автор: kisilevartem228


\sqrt{3x + 1} = 3x - 1
помогите решить пожалуйста уравнение!​

Ответы

Автор ответа: Аноним
1

ОДЗ: \displaystyle \left \{ {{3x+1\geq 0} \atop {3x-1\geq 0}} \right.~~\Rightarrow~~\left \{ {{x\geq -\frac{1}{3}} \atop {x\geq \frac{1}{3}}} \right.~~\Rightarrow~~ x\geq \frac{1}{3}

Возводим обе части уравнения в квадрат, получим

3x+1=(3x-1)^2\\ \\ 3x+1=9x^2-6x+1\\ \\ 9x^2-9x=0\\ \\ 9x(x-1)=0\\ \\ x_1=0\\ \\ x_2=1

Корень x = 0 не удовлетворяет ОДЗ.

Ответ: x = 1.

kisilevartem228: Душевно
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