Question

При каких значениях переменной x дробь     х               не имеет смысла?                                                                         --------                                                                         x^2-4

Answer 1

Дробь не имеет смысла тогда, когда её знаменатель равень нулю.

Поэтому, чтобы найти указанные в задании значения, решаем уравнение:

x^2-4=0

x^2=4

x= -2 или x=2

Ответ: при x= -2, x=2.

Удачи вам!

Answer 2

To find the values of x for which the expression x^2 - 4 does not have meaning (i.e., is undefined), we need to consider the cases where the expression results in a division by zero or other undefined operations.

In the expression x^2 - 4, there is no division operation involved, so the only case where the expression does not have meaning is when there is a square root of a negative number. This is because taking the square root of a negative number is not defined in the real number system.

So, to find the values of x where the expression x^2 - 4 does not have meaning, we need to find the values of x for which x^2 - 4 < 0 (i.e., the expression inside the square root is negative). In other words:

x^2 - 4 < 0

Now, let's solve for x:

x^2 - 4 < 0 x^2 < 4

Now we can factor the left-hand side:

(x - 2)(x + 2) < 0

To determine the solution, we create a sign chart by considering the sign of the expression (x - 2)(x + 2) for different intervals of x:

Intervals: (-∞, -2) (-2, 2) (2, ∞) (x - 2)(x + 2): - | + | +

From the sign chart, we see that the expression (x - 2)(x + 2) is negative in the interval (-2, 2). Therefore, the values of x for which the expression x^2 - 4 does not have meaning (i.e., is undefined) are within the interval (-2, 2).

In summary, the values of x for which the expression x^2 - 4 does not have meaning are x < -2 and x > 2. At these points, the expression results in taking the square root of a negative number, which is not defined in the real number system.