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Ryan, Engineer
Category: Homework
Satisfied Customers: 8982
Experience:  B.S. in Civil Engineering
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# tom thats nor right it should be three points on the curve

### Customer Question

tom thats nor right it should be three points on the curve no?
Submitted: 5 years ago.
Category: Homework
Expert:  Tom replied 5 years ago.

Not necessarily, there are maximum 3 but not necessarily 3 points. However, I see that I have indeed made an error, for which I'm very sorry. The correct answer should be:

The points of intersection can be found for those values x when:

1/2 x³ + x² + 1 = 9x² - 57/2 x +1

=> 1/2 x³ - 8x² + 57/2x = 0

=> x (x² - 16x + 57) = 0

=> x = 0 or x = 8+√7 or x = 8-√7

So there are indeed 3 points of intersection: (0,1) , (8+√7, 412 + 231/2 √7) and (8-√7, 412 - 231/2 √7) (or with rounded numbers (0,1), (10.646, 717.584) and (5.354, 106.416) )

Again my apologies for this error (no need to accept this answer off course!)

Best regards,

Tom

Customer: replied 5 years ago.
No tom,, its still not correct it says,
Customer: replied 5 years ago.
Customer: replied 5 years ago.