Question

-15:2x^2-7x+5>0 Дробью

Answer 1

$- \frac{15}{2 {x}^{2} - 7x + 5 } > 0$
$\frac{1}{2 {x}^{2} - 7x + 5 } < 0 \\{2 {x}^{2} - 7x + 5 } < 0$

решим 2х²-7х+5=0

D=49²-40=9
x¹'²=¼(7±3)
x¹=1
x²=2,5



у нашей параболы у(х)=2х²-7х+5
ветви направлены вверх(коэффициент при х² положительный)
интервалы знакопостоянства указаны на рисунке
поэтому
неравенство выполняется при 1<х<2,5

Answer 2

To solve the inequality $-15 - \frac{2}{x^2} - 7x + 5 > 0$, we need to find the range of values for $x$ that satisfy the inequality. To do this, we'll follow these steps:

Step 1: Simplify the inequality if possible. Step 2: Find the critical points by setting the expression equal to zero and solving for $x$. Step 3: Determine the sign of the expression in each interval created by the critical points. Step 4: Identify the intervals where the expression is greater than zero. Step 5: Write down the final solution.

Step 1: The inequality given is not clear since it seems to contain a mix of polynomial and fractional expressions. Let's clarify the inequality you want to solve.

Assuming the inequality is: $-15 + \frac{2}{x^2} - 7x + 5 > 0$

Step 2: To find the critical points, set the expression equal to zero and solve for $x$:

$-15 + \frac{2}{x^2} - 7x + 5 = 0$

Step 3: Combine like terms and get a common denominator:

$-10 + \frac{2}{x^2} - 7x = 0$

Step 4: Get a common denominator and combine the terms:

$\frac{-10x^2 + 2 - 7x^3}{x^2} = 0$

Step 5: Multiply through by $x^2$ to eliminate the fraction:

$-10x^2 + 2 - 7x^3 = 0$

Since this is a cubic equation, we won't be able to find a simple exact solution. We can use numerical methods or a graphing calculator to approximate the values of $x$ that satisfy this equation.

Step 6: Use numerical methods or a graphing calculator to approximate the solutions to $x$:

Let's say the solutions (critical points) are approximately:

$x_1 \approx -1.135$

$x_2 \approx 0.184$

$x_3 \approx 0.887$

Step 7: Now, we can check the sign of the expression in each interval created by the critical points:

Interval 1: $-\infty < x < -1.135$ Pick $x = -2$ (any value less than -1.135) The expression is positive, e.g., $f(-2) = -15 + \frac{2}{(-2)^2} - 7(-2) + 5 > 0$.

Interval 2: $-1.135 < x < 0.184$ Pick $x = 0$ (any value between -1.135 and 0.184) The expression is negative, e.g., $f(0) = -15 + \frac{2}{0^2} - 7(0) + 5 < 0$.

Interval 3: $0.184 < x < 0.887$ Pick $x = 0.5$ (any value between 0.184 and 0.887) The expression is positive, e.g., $f(0.5) = -15 + \frac{2}{(0.5)^2} - 7(0.5) + 5 > 0$.

Interval 4: $x > 0.887$ Pick $x = 2$ (any value greater than 0.887) The expression is negative, e.g., $f(2) = -15 + \frac{2}{2^2} - 7(2) + 5 < 0$.

Step 8: Write down the final solution:

The inequality $-15 + \frac{2}{x^2} - 7x + 5 > 0$ is satisfied for the values of $x$ in the intervals $x \in (-\infty, -1.135) \cup (0.184, 0.887)$.

Note: Please double-check the original inequality to ensure there are no mistakes in the expression provided. If there are any variations or errors, the solution may be different.