Question

X²+3x-Vx³+3 x - 2 = 0​

Answer 1

Ответ: x₁=-4,  x₂=1.

Пошаговое объяснение:

ОДЗ:

$x^2+3x\geq 0\\\\x*(x+3)\geq 0$

-∞____-3____0____+∞

$x\in(-\infty;-3]U[0;+\infty).$

$x^2+3x-\sqrt{x^2+3x}-2 =0\\\\\sqrt{x^2+3x} =t\geq 0\\\\t^2-t-2=0\\\\t^2-2t+t-2=0\\\\t*(t-2)+(t-2)=0\\\\(t-2)*(t+1)=0\\\\t-2=0\\\\t_1=\sqrt{x^2+3x}=2\\\\(\sqrt{x^2+3x})^2=2^2\\\\x^2+3x=4\\\\x^2+3x-4=0\\\\x^2+4x-x-4=0\\\\x*(x+4)-(x+4)=0\\\\(x+4)*(x-1)=0\\\\x+4=0\\\\x_1=-4.\\\\x-1=0\\\\x_2=1.\\\\t+1=0\\\\t_1=\sqrt{x^2+3x} =-1\notin.\ \ \ \ \ \ \Rightarrow$