Question

4-x^2>(2+x)^2 СРОЧНО!!!

Answer 1

Ответ:

х Є 《 - 2 ; 0 》

Пошаговое объяснение:

4 - x² > ( 2 + x )²

( 2 - x ) × ( 2 + x ) > ( 2 + x )²

( 2 - x ) × ( 2 + x ) - ( 2 + x )² > 0

( 2 + x ) × ( 2 - x - ( 2 + x ) ) > 0

( 2 + x ) × ( 2 - x - 2 - x ) > 0

( 2 + x ) × ( - 2x ) > 0

Система

2 + x > 0

- 2x > 0

Система

2 + x < 0

- 2x < 0

Система

x > - 2

x < 0

Система

x < - 2

x > 0

x Є 《 - 2 ; 0 》

х Є порожня множина

х Є 《 - 2 ; 0 》

Answer 2

Вітаю.

Відповідь: (-2;0)

Розв'язання Завдання додаю.

Answer 3

To solve the inequality 4-x^2 > (2+x)^2, we can start by expanding the right side of the inequality:

(2+x)^2 = (2+x)(2+x) = 4 + 2x + 2x + x^2 = 4 + 4x + x^2

Now, let's rewrite the inequality:

4 - x^2 > 4 + 4x + x^2

Next, let's simplify the inequality by combining like terms:

-x^2 > 4x + 8

To solve this inequality, we can move all the terms to one side of the inequality sign:

-x^2 - 4x - 8 > 0

Now, let's find the roots of the quadratic equation by setting the inequality to zero:

-x^2 - 4x - 8 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -1, b = -4, and c = -8. Plugging these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)^2 - 4(-1)(-8))) / (2(-1))

Simplifying further:

x = (4 ± √(16 - 32)) / (-2)

x = (4 ± √(-16)) / (-2)

Since the discriminant (√(16 - 32)) is negative, the quadratic equation has no real solutions. Therefore, the inequality 4-x^2 > (2+x)^2 is true for all real values of x.

Please note that the above explanation is based on mathematical calculations and does not cite any external sources.