Question

X2+17x>-72 решить неравенство

Answer 1

1234567890йцукенгшщзхфывапролджэячсмитьбю

Answer 2

To solve the inequality $x^2 + 17x > -72$, we'll follow these steps:

1. Move all terms to one side of the inequality to get a quadratic inequality in the form $ax^2 + bx + c > 0$.
2. Factorize (if possible) or use the quadratic formula to find the critical points of the inequality.
3. Determine the sign of the quadratic expression in different intervals.
4. Find the solution by identifying the intervals where the expression is greater than zero.

Let's go through each step:

1. Move all terms to one side of the inequality: $x^2 + 17x + 72 > 0$

2. Factorize the quadratic expression: We need to find two numbers whose sum is 17 and whose product is 72. Those numbers are 8 and 9, as $8 + 9 = 17$ and $8 \times 9 = 72$. Now, rewrite the expression as: $(x + 8)(x + 9) > 0$

3. Determine the critical points (where the expression equals zero): Set each factor to zero and solve for $x$: $x + 8 = 0 \implies x = -8$ $x + 9 = 0 \implies x = -9$

4. Determine the sign of the expression in different intervals: We'll use a sign chart to analyze the inequality:

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Interval       | x + 8   | x + 9   | (x + 8)(x + 9)
------------------------------------------------
x < -9         |   -     |   -     |    +
-9 < x < -8    |   -     |   +     |    -
x > -8         |   +     |   +     |    +

5. Find the solution: From the sign chart, we see that the expression $(x + 8)(x + 9)$ is greater than zero in two intervals: $x < -9$ and $x > -8$. This means the solution to the original inequality is: $x < -9 \text{ or } x > -8$

In interval notation, the solution is $(- \infty, -9) \cup (-8, \infty)$.