Question

A(-1;x), B(2x;-3), AB=7. x-?​

Answer 1

Проверьте условие, там должно быть для точки В 3, а не минус 3. В противном случае х принимает иррациональное значение.

(2х+1)^2+(3-х)^2=7^2

4х^2+4х+1+9-6х+х^2=49

5х^2-2х-39=0

D=4+4*5*39=784

x =(2-28)/10=-2,6

x=(2+28)/10=3

Ответ : - 2,6 и 3.

Answer 2

To find the value of x, we can use the distance formula for two points in a Cartesian plane. The distance formula between two points (x1, y1) and (x2, y2) is given by:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, we have two points A(-1, x) and B(2x, -3), and the distance AB is given as 7 units. We can set up the distance formula equation:

AB = √((2x - (-1))^2 + (-3 - x)^2)

Now, we can solve for x:

7 = √((2x + 1)^2 + (-3 - x)^2)

Square both sides to eliminate the square root:

49 = (2x + 1)^2 + (-3 - x)^2

Expand the squares:

49 = 4x^2 + 4x + 1 + x^2 + 6x + 9

Combine like terms:

49 = 5x^2 + 10x + 10

Rearrange to form a quadratic equation:

5x^2 + 10x + 10 - 49 = 0

5x^2 + 10x - 39 = 0

Now, we can solve this quadratic equation using any method. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 5, b = 10, and c = -39.

x = (-(10) ± √(10^2 - 4 * 5 * -39)) / 2 * 5

x = (-10 ± √(100 + 780)) / 10

x = (-10 ± √880) / 10

Now, calculate the two possible values of x:

x = (-10 + √880) / 10 ≈ 0.732

x = (-10 - √880) / 10 ≈ -1.532

So, there are two possible values of x: approximately 0.732 and approximately -1.532.