Question

Знайдіть множину розв'язків нерівності:
$4( {b}^{2} - 4) - 4b(b + 2) < 9$
$\frac{2x}{5} - \frac{x - 1}{15} > 0$
$3x + 12 > 2(4x - 3) - 5x$



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Answer 1

Ответ:

To solve the inequality 4b^2 - 4(b+2) < 9, we first distribute the -4 to get:

4b^2 - 4b - 8 < 9

Next, we move all the terms to one side to get a quadratic inequality:

4b^2 - 4b - 8 - 9 < 0

Simplifying further, we have:

4b^2 - 4b - 17 < 0

To solve this inequality, we can use the quadratic formula. The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = 4, b = -4, and c = -17. Plugging these values into the quadratic formula, we get:

b = (-(-4) ± √((-4)^2 - 4(4)(-17))) / (2(4))

Simplifying further:

b = (4 ± √(16 + 272)) / 8

b = (4 ± √288) / 8

b = (4 ± 16.97) / 8

Now we have two possible solutions for b:

b = (4 + 16.97) / 8 ≈ 2.87

b = (4 - 16.97) / 8 ≈ -1.37

Therefore, the solution to the inequality 4b^2 - 4(b+2) < 9 is approximately -1.37 < b < 2.87.

Объяснение:

сори то что на английском