(x^2-11)(11+x^2) 7^x-1-6^2-2x=0 |x^2-5x|<6

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вопрос

To solve the inequality |x^2-5x|<6, we will break it down into two separate inequalities and solve them individually.

x^2-5x < 6
Rearranging the inequality, we get:
x^2 - 5x - 6 < 0
Factoring the quadratic equation, we get:
(x-6)(x+1) < 0
This inequality is true when x is between -1 and 6.

x^2-5x > -6
Rearranging the inequality, we get:
x^2 - 5x + 6 > 0
Factoring the quadratic equation, we get:
(x-2)(x-3) > 0
This inequality is true when x is less than 2 or greater than 3.

Combining the solutions from both inequalities, we find that |x^2-5x|<6 is true for x values that are between -1 and 2, or between 3 and 6.

Therefore, the solution to the inequality |x^2-5x|<6 is -1 < x < 2 or 3 < x < 6.