Thread: Coordinates of points of intersection

1. Coordinates of points of intersection

Find the coordinates of points of intersection of $\displaystyle y=\frac{1}{x^2}$ and $\displaystyle y=3x+7$

2. Have you tried anything at all? At a "point" of intersection, (x,y) the coordinates must satisfy both equations so

$\displaystyle y= \frac{1}{x^2}= 3x+ 7$.

Solve that equation for x and then use either of the given equations to find y.

The equation for x will be a cubic polynomial that has no rational roots so solving it is going to be difficult.

3. Originally Posted by HallsofIvy
Have you tried anything at all? At a "point" of intersection, (x,y) the coordinates must satisfy both equations so
$\displaystyle y= \frac{1}{x^2}= 3x+ 7$. Soklve that equation for x and then use either of the given equations to find y.

The equation for x will be a cubic polynomial that has no rational roots so solving it is going to be difficult.
The only thing I could think was was equating $\displaystyle \frac{1}{x^2}= 3x+ 7$ but I couldn't solve it

4. Originally Posted by Punch
The only thing I could think was was equating $\displaystyle \frac{1}{x^2}= 3x+ 7$ but I couldn't solve it
Are you expected to solve by hand or use a Computer Algebra System? It helps to know the background to the question.

5. i have no knowledge of computer algebra so i assume i have to solve it by hand. but i couldn't solve the question either

6. Originally Posted by Punch
i have no knowledge of computer algebra so i assume i have to solve it by hand. but i couldn't solve the question either
The fact that you have no knowledge doesn't mean that's not how it's meant to be done. I suggest you discuss the question with your instructor.

The alternative is to do it by hand by applying an iterative procedure (but I suppose you would have no knowledge of how to do this either).

Until you can clarify the expectations of the person who set this question, it is pointless discussing the question further.