Question

Не выполняя построения графиков функции y=8/x и y=x/2, найдите координаты точек их пересечения

Answer 1

8/x=x/2
x^2=16
x=4 x=-4
y=8/4=2           y=4/2=2
y=8/(-4)=-2           y=-4/2=-2
(4;2) (-4;-2)

Answer 2

Finding the Intersection Points of the Functions y = 8/x and y = x/2

To find the coordinates of the intersection points between the functions y = 8/x and y = x/2, we need to set the two equations equal to each other and solve for x.

Setting y = 8/x equal to y = x/2, we have:

8/x = x/2

To solve this equation, we can cross-multiply:

2 * 8 = x * x

16 = x^2

Taking the square root of both sides, we get:

x = ±√16

x = ±4

Now that we have the x-values, we can substitute them back into either of the original equations to find the corresponding y-values.

For x = 4, substituting into y = 8/x, we have:

y = 8/4 = 2

So one intersection point is (4, 2).

For x = -4, substituting into y = 8/x, we have:

y = 8/(-4) = -2

So the other intersection point is (-4, -2).

Therefore, the coordinates of the intersection points between the functions y = 8/x and y = x/2 are (4, 2) and (-4, -2).