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

Answer 2

Answer:

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

Step-by-step explanation:

we have

$y=x^{2}$ ----> equation A

$y=\frac{1}{x} +2$ -----> 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