Question

Решить неравенство 25x^2> 49

Answer 1

Ответ:

Объяснение:

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Answer 2

To solve the inequality $25x^2 > 49$, follow these steps:

Step 1: Subtract 49 from both sides to move all terms to one side of the inequality: $25x^2 - 49 > 0$

Step 2: Factor the quadratic expression if possible: $25x^2 - 49 = (5x)^2 - 7^2 = (5x - 7)(5x + 7)$

Step 3: Now, the inequality becomes: $(5x - 7)(5x + 7) > 0$

Step 4: Determine the critical points. The critical points are the values of $x$ that make the expression inside the parentheses zero: $5x - 7 = 0 \Rightarrow 5x = 7 \Rightarrow x = \frac{7}{5}$ $5x + 7 = 0 \Rightarrow 5x = -7 \Rightarrow x = -\frac{7}{5}$

Step 5: Create a sign chart and test the intervals between and outside the critical points to find the solution:

scssCopy code
           -∞         -7/5        7/5         +∞
     ----------------------------------------------
      (5x - 7)(5x + 7)    |   -     |   +    |   +
      25x^2 - 49          |   -     |   +    |   +

Step 6: Determine the solution based on the sign chart: The inequality is satisfied when $(5x - 7)(5x + 7) > 0$, which means that the expression is positive.

From the sign chart, we can see that the expression is positive for $x < -\frac{7}{5}$ and $x > \frac{7}{5}$.

So, the solution to the inequality $25x^2 > 49$ is $x < -\frac{7}{5}$ or $x > \frac{7}{5}$.