Question

X2+5x>36 квадратные неравенства

Answer 1

Смотри...............

Answer 2

To solve the quadratic inequality $x^2 + 5x > 36$, we can follow these steps:

Step 1: Move all terms to one side of the inequality to set it to zero. $x^2 + 5x - 36 > 0$

Step 2: Factorize the quadratic expression (if possible). $x^2 + 5x - 36 = (x + 9)(x - 4)$

Step 3: Find the critical points by setting the expression inside the brackets to zero. $x + 9 = 0 \quad \text{and} \quad x - 4 = 0$

Solving for $x$ in each case: $x = -9 \quad \text{and} \quad x = 4$

Step 4: Create a sign chart or number line using the critical points. We have three intervals: $(- \infty, -9)$, $(-9, 4)$, and $(4, \infty)$.

Step 5: Test a point in each interval to determine the sign of the quadratic expression in that interval. For example, let's use $x = 0$ in each interval:

• $x = 0$ in $(- \infty, -9)$: $(0 + 9)(0 - 4) = (9)(-4) = -36 < 0$ (negative)
• $x = 0$ in $(-9, 4)$: $(0 + 9)(0 - 4) = (9)(-4) = -36 < 0$ (negative)
• $x = 0$ in $(4, \infty)$: $(0 + 9)(0 - 4) = (9)(0 - 4) = -36 < 0$ (negative)

Step 6: Determine the solution based on the sign chart. The inequality $x^2 + 5x - 36 > 0$ is true for $x$ in the intervals $(- \infty, -9)$ and $(4, \infty)$.

Step 7: Express the solution in interval notation. The solution is: $-\infty < x < -9$ or $x > 4$.