Question

2х*-11х+23>(х-5)*Решите неравенство *- это обозначает в квадрате

Answer 1

2x^2-11x+23>(x-5)^2

2x^2-11x+23>x^2-10x+25

x^2-x-2>0

D=-1^2-4*1*-2=9   √D=3
x1=(1-3)/(2*1)=-1
x2=(1+3)/(2*1)=2
Ответ: (-∞;-1)v(2;+∞)

Answer 2

2x^2-11x+23>x^2-10x+25
x^2-x-2>0
D=1+8=9
x1=1-3/2=-1
x2=1+3/2=2

Answer 3

Solving the Inequality

To solve the given inequality 2x^2 - 11x + 23 > (x - 5)^2, we can follow these steps:

1. Expand and simplify the right-hand side of the inequality. 2. Set the inequality to zero and find the roots of the quadratic equation. 3. Use the roots to determine the intervals where the inequality is satisfied.

Step 1: Expand and Simplify

First, let's expand and simplify the right-hand side of the inequality (x - 5)^2:

(x - 5)^2 = x^2 - 10x + 25

Now, the inequality becomes 2x^2 - 11x + 23 > x^2 - 10x + 25.

Step 2: Set the Inequality to Zero and Find the Roots

Next, let's set the inequality to zero and find the roots of the quadratic equation:

2x^2 - 11x + 23 - x^2 + 10x - 25 > 0

This simplifies to x^2 - x - 2 > 0.

The roots of the quadratic equation x^2 - x - 2 = 0 can be found using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = -1, and c = -2.

The roots are: x = (-(-1) ± √((-1)^2 - 4*1*(-2))) / (2*1) x = (1 ± √(1 + 8)) / 2 x = (1 ± √9) / 2 x = (1 ± 3) / 2 x = (1 + 3) / 2 = 4 / 2 = 2 x = (1 - 3) / 2 = -2 / 2 = -1

So, the roots are x = 2 and x = -1.

Step 3: Determine the Intervals

Now, we can determine the intervals where the inequality is satisfied. We can do this by plotting the roots on a number line and testing the inequality in each interval.

The inequality x^2 - x - 2 > 0 is satisfied when x < -1 or x > 2.

Therefore, the solution to the inequality 2x^2 - 11x + 23 > (x - 5)^2 is x < -1 or x > 2.

This means that the inequality is satisfied when x is less than -1 or greater than 2.