Question

Equations y1 = x2 − 5x + 8 and y2=10/x intersect at a point. What is the closest value of x when y1 = y2?

A.
between 3 and 3.5
B.
between 3 and 4
C.
between 3.5 and 4
D.
between 3.5 and 4.5

Answer 1

C. between 3.5 and 4

Explanation:

We are given

`y_1=x^2-5x+8`

`y_2=(10)/(x)`

Since, we have to solve for x

so, firstly we will set them equal

`x^2-5x+8=(10)/(x)`

we can multiply both sides by x

and we get

`x^3-5x^2+8x=10`

now, we can use graphing calculator

and find intersection point between y1 and y2

so, we can see that

x=3.538 lies between 3.5 and 4

so,

C. between 3.5 and 4