Question

Решите методом интервалов :

Answer 1

$\cfrac{3x+1}{x-2} \geq 2 \\\ \cfrac{3x+1-2(x-2)}{x-2} \geq 0 \\\ \cfrac{3x+1-2x+4}{x-2} \geq 0 \\\ \cfrac{x+5}{x-2} \geq 0 \\\ x\in(-\infty;-5]\cup(2;+\infty)$

Answer 2

Solving the Equation Using Interval Method

To solve the equation using the interval method, we need to find the intervals where the equation is greater than zero.

Let's consider the equation: 6x^2 - 7x + 20 > 0.

To solve this equation, we can use the factored form of the quadratic equation. However, since the given equation does not factor easily, we can use the quadratic formula to find the roots of the equation.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation 6x^2 - 7x + 20 > 0, the coefficients are: - a = 6 - b = -7 - c = 20

Using the quadratic formula, we can find the roots of the equation:

x = (-(-7) ± √((-7)^2 - 4 * 6 * 20)) / (2 * 6)

Simplifying the equation gives us:

x = (7 ± √(49 - 480)) / 12

x = (7 ± √(-431)) / 12

Since the discriminant (√(-431)) is negative, the equation has no real roots. Therefore, there are no intervals where the equation 6x^2 - 7x + 20 > 0 is greater than zero.

In conclusion, the equation 6x^2 - 7x + 20 > 0 has no solution.