The graphs of y = 120/x and y = 120 - 20x intersect

Question

at two points.

Write down the coordinates of these two points

Answer 1

To find the coordinates of the points of intersection, we can set the two equations equal to each other and solve for x:

120/x = 120 - 20x

Multiplying both sides by x:
120 = 120x - 20x^2

Rearranging the equation to set it equal to zero:
20x^2 - 120x + 120 = 0

Dividing the equation by 20 to simplify:
x^2 - 6x + 6 = 0

Now we can use the quadratic formula to solve for x:
x = [6 ± sqrt((-6)^2 - 4*1*6)] / 2
x = [6 ± sqrt(36 - 24)] / 2
x = [6 ± sqrt(12)] / 2
x = [6 ± 2sqrt(3)] / 2
x = 3 ± sqrt(3)

Therefore, the coordinates of the two points of intersection are:
(3 + sqrt(3), 120/(3 + sqrt(3))) and (3 - sqrt(3), 120/(3 - sqrt(3))).

These coordinates can be simplified further by rationalizing the denominators.