Question

At what points are the equations y=x2 and y=1/x+2 equal?

Answer 1

Try this:
1) If y=x² and y=(2x+1)/x, then

`x^2= (2x+1)/(x); \ \ \textless \ =\ \textgreater \ \ x^3-2x-1=0; \ (x \\eq 0)` <=>
`(x+1)(x^2-x-1)=0; \ (x \\eq 0)\ \ \textless \ =\ \textgreater \ \left[\begin{array}{ccc}x=-1\\x= (1+ √(5) )/(2) \\x= (1- √(5))/(2) \end{array}\right`
2) after 'x' are found it need to calculate 'y':
Answer: (-1;1), (-0.618;0.382), (1.618;2.618)

Answer 2

`(-1,1),(-0.618,0.382), (1.618,2.618)`

Explanation:

we have

`y=x^(2)` ----> equation A

`y=(1)/(x) +2` -----> equation B

we know that

The intersection points both graphs are the points where both equations have the same value

so

Using a graphing tool

The intersection points are
`(-1,1),(-0.618,0.382), (1.618,2.618)`

see the attached figure