Consider the problem: Cube equal squares and number. Use al Khayyami's method and identify two conic sections whose intersection yields the solution (give the equations of the curves, and indicate whether they are circles, parabolas, hyperbolas, or ellipses). • Sketch a figure showing the two curves. (The use of GeoGebra is recommended) ● Will the curves always intersect, regardless of the coefficients? ● Suggestion: Treat the problem as x³ = px² + pq², where p, q are lengths, and use the curve 2 Py = = x².
Consider the problem: Cube equal squares and number. Use al Khayyami's method and identify two conic sections whose intersection yields the solution (give the equations of the curves, and indicate whether they are circles, parabolas, hyperbolas, or ellipses). • Sketch a figure showing the two curves. (The use of GeoGebra is recommended) ● Will the curves always intersect, regardless of the coefficients? ● Suggestion: Treat the problem as x³ = px² + pq², where p, q are lengths, and use the curve 2 Py = = x².
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the problem: Cube equal squares and number.
• Use al Khayyami's method and identify two conic sections whose intersection yields the solution (give
the equations of the curves, and indicate whether they are circles, parabolas, hyperbolas, or ellipses).
• Sketch a figure showing the two curves. (The use of GeoGebra is recommended)
Will the curves always intersect, regardless of the coefficients?
Suggestion: Treat the problem as x³ = px² + pq², where p, q are lengths, and use the curve py = x².
2
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