Question

РЕшите неравенство x²-36<0​

Answer 1

Решение:

x²-36=0

(x-6)(x+6)=0

x-6=0       x+6=0

x=6           x=-6

Ответ: 6, -6

Answer 2

To solve the inequality $x^2 - 36 < 0$, follow these steps:

Step 1: Factor the left-hand side (LHS) of the inequality, if possible. $x^2 - 36 = (x - 6)(x + 6)$

Step 2: Find the critical points by setting each factor equal to zero and solving for $x$. $x - 6 = 0 \implies x = 6$ $x + 6 = 0 \implies x = -6$

Step 3: Create a number line and plot the critical points on it.

luaCopy code
          -∞  -6  6  +∞
          |---|---|---|

Step 4: Test a point in each region of the number line to determine the sign of the expression $x^2 - 36$.

• For $x < -6$, let's choose $x = -10$ (any value less than -6 will work). $x^2 - 36 = (-10)^2 - 36 = 100 - 36 = 64 > 0$, so it's positive in this region.

• For $-6 < x < 6$, let's choose $x = 0$ (any value between -6 and 6 will work). $x^2 - 36 = (0)^2 - 36 = -36 < 0$, so it's negative in this region.

• For $x > 6$, let's choose $x = 10$ (any value greater than 6 will work). $x^2 - 36 = (10)^2 - 36 = 100 - 36 = 64 > 0$, so it's positive in this region.

Step 5: Determine the solution set based on the sign of $x^2 - 36$.

The inequality is $x^2 - 36 < 0$, meaning we are looking for the values of $x$ that make the expression negative. From the number line, we see that $x$ must be between -6 and 6 (excluding -6 and 6).

So, the solution to the inequality is $-6 < x < 6$.