Question

Докажите,что выражение 4х²-4х-3 может принимать лишь отрицательные значения ​

Answer 1

Это неверное утверждение. Например, при x=2:

4·2² – 4·2 – 3 = 16 – 8 – 3 = 5 > 0

Answer 2

Proof that the expression 4x² - 4x - 3 can only take negative values

To prove that the expression 4x² - 4x - 3 can only take negative values, we need to show that it is always less than zero for any value of x.

Let's start by factoring the expression:

4x² - 4x - 3 = (2x - 3)(2x + 1)

Now, we can analyze the factors individually to determine the conditions under which the expression is negative.

1. (2x - 3): - For this factor to be negative, we need 2x - 3 < 0. - Solving this inequality, we find x < 3/2.

2. (2x + 1): - For this factor to be negative, we need 2x + 1 < 0. - Solving this inequality, we find x < -1/2.

To ensure that both factors are negative, we need x to satisfy both conditions simultaneously. Therefore, the expression 4x² - 4x - 3 will be negative when x < -1/2 and x < 3/2.

In conclusion, the expression 4x² - 4x - 3 can only take negative values when x is less than -1/2 and 3/2.