line y33 curve y2x512 they both at a point how to find the x

line y=33

curve y=(2x-5)^1/2

they both at a point how to find the x axis at the point of intersection

please explained clearly

in normal writing

no cursive

Solution

Observe the question. It gives two equations. On point of intersection, both equations will be such that they will have common coordinates. The coordinate of the line of intersection will belong to born the equations. Let the coordinates be (x, y).

Then y=3(3)^0.5

& y=(2x-5)^1/2

Squaring born equations and equating the y coordinates

2x-5=(3(3)^1 /2) ^2

Or,2x-5=27

Or,2x=27+5=32

Or,x=32/2=16

Thus,x=16 and y=3(3)^0.5

This will be the coordinate of the point of intersection.

(16,3(3)^0.5)