Question

Решить уравнение: √(2x^2+2x-1)=-x-1

Answer 1

Ответ:

x=-√2

Объяснение:

$\sqrt{(2x^{2} +2x-1)} =-x-1\\ \sqrt{(2x^{2} +2x-1)}^{2}  =(-x-1)^{2} \\ 2x^{2} +2x-1  =(-(x+1))^{2} \\ 2x^{2} +2x-1  =(x+1)^{2} \\ 2x^{2} +2x-1  =x^{2} +2x+1 \\ 2x^{2} -1  =x^{2} +1 \\ 2x^{2} -1  =x^{2} +1 \\ 2x^{2} -x^{2} =1+1\\ x^{2} =2\\ x^{2} =+-\sqrt{2} \\ x=-\sqrt{2} , x=\sqrt{2} \\ \sqrt{2(-\sqrt{2})^{2}  +2(-\sqrt{2} )-1} =-(-\sqrt{2} )-1, \sqrt{2*\sqrt{2}^{2} +2\sqrt{2} -1 } =-\sqrt{2} -1\\ 0.414214=0.414214, 2.41421=-2.41421\\ x=-\sqrt{2} ,x\neq \sqrt{2} \\ x=-\sqrt{2}$

Answer 2

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