Question

Укажите число не являющейся решением неравенства x2-4x+4 >0

Answer 1

x²-4x+4>0

(x-2)²>0

поскольку неравенство строгое, то решением будут являться все числа, кроме 2

Answer 2

To find the numbers that are not solutions to the inequality $x^2 - 4x + 4 > 0$, we need to first solve the inequality and then identify the values that do not satisfy it.

Step 1: Solve the inequality $x^2 - 4x + 4 > 0$.

To solve this quadratic inequality, we can factor it as follows:

$x^2 - 4x + 4 = (x - 2)^2$

Since the square of any real number is always non-negative, the expression $(x - 2)^2$ is greater than or equal to zero for all real values of $x$. Therefore, the inequality $x^2 - 4x + 4 > 0$ is only satisfied when $(x - 2)^2$ is greater than zero.

Step 2: Identify the values of $x$ that do not satisfy $x^2 - 4x + 4 > 0$.

The inequality $(x - 2)^2 > 0$ holds true for all real values of $x$ except when $(x - 2)^2 = 0$. So, to find the number that is not a solution to the inequality, we set $(x - 2)^2 = 0$ and solve for $x$:

$(x - 2)^2 = 0$

Taking the square root of both sides:

$x - 2 = 0$

Solving for $x$:

$x = 2$

The number that is not a solution to the inequality $x^2 - 4x + 4 > 0$ is $x = 2$. For any other real value of $x$, the inequality is satisfied.