Question

(x-4)(x+3)-(x-6)(x+6)>10​

Answer 1

Как то так! Надеюсь помогла!

Answer 2

Let's start by simplifying the given inequality step by step:

1. Expand the expressions within the parentheses: (x - 4)(x + 3) - (x - 6)(x + 6) > 10

   Expand the first term: x^2 - 4x + 3x - 12 Expand the second term: x^2 + 6x - 6x - 36

   This simplifies to: x^2 - 12 - 36

2. Combine like terms: x^2 - 48

Now, we have the inequality: x^2 - 48 > 10

3. Add 48 to both sides of the inequality: x^2 > 58

4. Take the square root of both sides: √(x^2) > √58 |x| > √58

This means that the absolute value of x must be greater than the square root of 58 for the given inequality to hold true. Therefore, the solution to the inequality is:

x > √58 or x < -√58

In interval notation, the solution can be written as: (-∞, -√58) U (√58, ∞)