Question

(x - 3)умножить на корень(14 + 5x - x ^ 2) <= 0​

Answer 1

(x-3)~(14+5x-x2)≥0
ОД3: 14+5×-×220
×2-5x-14≤0
×2-5x-14=0
D=(-5)2 -4*4-14)=25+56=81=92
X=(5-91/2=-4/2=-2
X=(5+9)/2=14/2=7
+
+
XE[-2; 7]
Неравенство решается только на промежутке [-2; 7]
×-3=0
X=3
†
-2 --------- 3 --== 7
при x=0
-
+ -
при x=4 + +1+
XE{-2}U[3; 7]
Ответ: {-2}U[3; 71.

Answer 2

To solve the inequality:

(x - 3) * sqrt(14 + 5x - x^2) <= 0

We can break it down into separate cases based on the sign of each factor and solve them individually.

1. Case: (x - 3) <= 0 and sqrt(14 + 5x - x^2) >= 0 In this case, both factors have the same sign. When x - 3 <= 0, it implies x <= 3. For the second factor, sqrt(14 + 5x - x^2) >= 0, the expression inside the square root must be non-negative. Thus, we have:

14 + 5x - x^2 >= 0 Rearranging the terms, we get: x^2 - 5x - 14 <= 0

Now, we can solve this quadratic inequality by factoring or using the quadratic formula. Factoring gives us: (x - 7)(x + 2) <= 0

To determine the solution, we can analyze the sign of each factor and find their intervals where the inequality holds:

x - 7 <= 0 and x + 2 >= 0 x <= 7 and x >= -2

The solution for the first case is -2 <= x <= 3.

2. Case: (x - 3) >= 0 and sqrt(14 + 5x - x^2) <= 0 Here, both factors have the same sign as well. When x - 3 >= 0, it implies x >= 3. For the second factor, sqrt(14 + 5x - x^2) <= 0, it means the expression inside the square root must be non-positive. Thus, we have:

14 + 5x - x^2 <= 0 Rearranging the terms: x^2 - 5x - 14 >= 0

Solving this quadratic inequality, we have: (x - 7)(x + 2) >= 0

Analyzing the sign of each factor, we find the intervals where the inequality holds:

x - 7 >= 0 and x + 2 <= 0 x >= 7 and x <= -2

The solution for the second case is x >= 3.

Combining the solutions from both cases, we have the final solution as: -2 <= x <= 3 or x >= 7