2,89 в степени (3х в степени 2 - 12) < 2,89 в степени (2х в степени 2 - х)

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вопрос

To solve this inequality, we can first simplify each side by expanding the exponents.

Left side:
2.89^(3x^2 - 12)

Right side:
2.89^(2x^2 - x)

Now, we need to compare the simplified forms of each side. Since the base is 2.89, we can compare the exponents directly.

3x^2 - 12 < 2x^2 - x

Subtract 2x^2 from both sides and add x to both sides:

x^2 + x - 12 < 0

Now we have a quadratic inequality. To solve this, we need to find the roots of the inequality by factoring or using the quadratic formula:

(x + 4)(x - 3) < 0

The roots of the inequality are x = -4 and x = 3. We can now test the intervals between these roots to determine when the inequality is true.

Since we are looking for when the expression is less than 0, the solution is:

-4 < x < 3

Therefore, the solution to the inequality is -4 < x < 3.