Question

X²+x⩾0 1)(-∞;-1]U[0;+∞} 2)[-1;0] 3)(-∞;0]U[1;+∞) 4)[-0;1]

Answer 1

Решаем методом интервалов. левую часть приравняем к нулю.

х*(х+1)=0

х=0; х+1=0; х=-1

_______-1____________0______

  +                            -                            +

х∈(-∞;-1]U[0;+∞}

Верный ответ 1)(-∞;-1]U[0;+∞}

Answer 2

1) (-∞; -1] U [0; +∞) This interval represents all the values of x for which x² + x is greater than or equal to 0. This includes all values less than or equal to -1 and all values greater than or equal to 0.

2) [-1; 0] This interval represents the values of x between -1 and 0. This interval is not included in the solution set because x² + x is not greater than or equal to 0 for values between -1 and 0.

3) (-∞; 0] U [1; +∞) This interval represents all the values of x for which x² + x is greater than or equal to 0. This includes all values less than or equal to 0 and all values greater than or equal to 1.

4) [-0; 1] This interval represents the values of x between 0 and 1. This interval is not included in the solution set because x² + x is not greater than or equal to 0 for values between 0 and 1.

In summary, the solution set for x² + x ≥ 0 is (-∞; -1] U [0; +∞) U (-∞; 0] U [1; +∞)