Question

X^2-1,44《0..........​

Answer 1

Ответ: х^2 меньше 1,44 или х меньше корня из 1,44 или х<|1,2¦ или -1,2<х<1,2.

Объяснение:

Answer 2

To solve the inequality $x^2 - 1.44 < 0$, we first need to find the critical points and determine the intervals where the inequality holds true.

Step 1: Factor the expression $x^2 - 1.44 = (x + 1.2)(x - 1.2)$

Step 2: Set each factor to zero and solve for critical points Setting $x + 1.2 = 0$, we get $x = -1.2$. Setting $x - 1.2 = 0$, we get $x = 1.2$.

Step 3: Determine the intervals

Now, we have three critical points: -1.2, 1.2, and 0 (since $0^2 - 1.44 = -1.44$). We need to test the inequality in each of the intervals created by these critical points.

Interval 1: $x < -1.2$ Pick a test point less than -1.2, e.g., -2. Substitute x = -2 into the inequality: $(-2)^2 - 1.44 < 0$. Simplifying, we get $4 - 1.44 < 0$, which is true.

Interval 2: $-1.2 < x < 0$ Pick a test point between -1.2 and 0, e.g., -1. Substitute x = -1 into the inequality: $(-1)^2 - 1.44 < 0$. Simplifying, we get $1 - 1.44 < 0$, which is false.

Interval 3: $0 < x < 1.2$ Pick a test point between 0 and 1.2, e.g., 0.5. Substitute x = 0.5 into the inequality: $(0.5)^2 - 1.44 < 0$. Simplifying, we get $0.25 - 1.44 < 0$, which is true.

Interval 4: $x > 1.2$ Pick a test point greater than 1.2, e.g., 2. Substitute x = 2 into the inequality: $2^2 - 1.44 < 0$. Simplifying, we get $4 - 1.44 < 0$, which is true.

Step 4: Final answer The inequality $x^2 - 1.44 < 0$ is true in the intervals $-1.2 < x < 0$ and $0 < x < 1.2$.

In interval notation, the solution to the inequality is: $(-1.2, 0) \cup (0, 1.2)$.