Question

X2-7x+12 меньше или равно 0

Answer 1

Вот здесь решила......

Answer 2

To solve the inequality $x^2 - 7x + 12 \leq 0$, we need to find the values of $x$ that satisfy the inequality. This can be done by factoring the quadratic expression or by using the quadratic formula.

Let's factor the expression first: $x^2 - 7x + 12 = (x - 3)(x - 4)$

Now, the inequality becomes: $(x - 3)(x - 4) \leq 0$

To find the values of $x$ that satisfy this inequality, we need to consider the sign of the expression $(x - 3)(x - 4)$ for different intervals of $x$.

1. When $x < 3$: Both $(x - 3)$ and $(x - 4)$ are negative. The product of two negatives is positive, so $(x - 3)(x - 4) > 0$ for $x < 3$.

2. When $x = 3$: Both $(x - 3)$ and $(x - 4)$ are zero, so $(x - 3)(x - 4) = 0$.

3. When $3 < x < 4$: $(x - 3)$ is positive, and $(x - 4)$ is negative. The product of a positive and a negative number is negative, so $(x - 3)(x - 4) < 0$ for $3 < x < 4$.

4. When $x = 4$: Both $(x - 3)$ and $(x - 4)$ are zero, so $(x - 3)(x - 4) = 0$.

5. When $x > 4$: Both $(x - 3)$ and $(x - 4)$ are positive. The product of two positives is positive, so $(x - 3)(x - 4) > 0$ for $x > 4$.

Now, we can put all this information together:

$(x - 3)(x - 4) \leq 0$ for $3 \leq x \leq 4$.

So, the solution to the inequality is $x$ belongs to the closed interval $[3, 4]$. In interval notation, the solution is $x \in [3, 4]$.