Question

3x^2 < 27 решить неравенство.

Answer 1

Ответ:

9<27

Объяснение:

${3x}^{2} = 9 \\ 9 < 27$

Answer 2

Ответ:

х^2=27/3

х^2=9

х1=3

х2=-3

вот помогла??))❤❤❤

Answer 3

To solve the inequality $3x^2 < 27$, we need to find the values of $x$ that satisfy the inequality. Here's the step-by-step solution:

Step 1: Subtract 27 from both sides of the inequality to isolate the quadratic term on the left side: $3x^2 - 27 < 0$

Step 2: Divide both sides by 3 to simplify the inequality: $x^2 - 9 < 0$

Step 3: Factor the quadratic expression on the left side, if possible. In this case, it's already factored: $(x + 3)(x - 3) < 0$

Step 4: Now, we need to find the critical points where the inequality might change its sign. Set each factor to zero and solve for $x$: $x + 3 = 0 \quad \text{and} \quad x - 3 = 0$

Solving for $x$: $x = -3 \quad \text{and} \quad x = 3$

Step 5: Create an inequality sign chart or a number line. Mark the critical points found in step 4 ($-3$ and $3$), and choose a test value from each of the intervals created by these critical points and plug it into the inequality to determine the sign in that interval.

Test value $x = -4$ (choose a value smaller than $-3$): $(x + 3)(x - 3) = (-4 + 3)(-4 - 3) = (-1)(-7) = 7 > 0$

Test value $x = 0$ (choose a value between $-3$ and $3$): $(x + 3)(x - 3) = (0 + 3)(0 - 3) = (3)(-3) = -9 < 0$

Test value $x = 4$ (choose a value greater than $3$): $(x + 3)(x - 3) = (4 + 3)(4 - 3) = (7)(1) = 7 > 0$

Step 6: Analyze the signs in each interval. We want the expression $(x + 3)(x - 3)$ to be less than zero ($0$) because that's the condition for the inequality $x^2 - 9 < 0$.

• For $x < -3$, $(x + 3)$ is positive and $(x - 3)$ is negative, so the product $(x + 3)(x - 3)$ is positive.
• For $-3 < x < 3$, $(x + 3)$ is positive, and $(x - 3)$ is also positive, so the product $(x + 3)(x - 3)$ is negative.
• For $x > 3$, $(x + 3)$ is positive, and $(x - 3)$ is negative, so the product $(x + 3)(x - 3)$ is positive.

Step 7: Finalize the solution. The inequality $x^2 - 9 < 0$ is satisfied for values of $x$ between $-3$ and $3$ (exclusive):

$-3 < x < 3$

So, the solution to the inequality is $x$ belonging to the open interval $(-3, 3)$.