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(a) Show that if two points. P (P₁. P₂). Q (9₁, 9₂) with Pr. Pz. 9. 19₂ € R the equation of the line through P and Q is of the form then ax+by =c with a, b, CER. (b) Derive from part (c) that if a line has two rational points, it has infinitely many rational points. P and Q have rational coordinates

(a) Show that if two points. P (P₁. P₂). Q (9₁, 9₂) with Pr. Pz. 9. 19₂ € R the equation of the line through P and Q is of the form then ax+by =c with a, b, CER. (b) Derive from part (c) that if a line has two rational points, it has infinitely many rational points. P and Q have rational coordinates

Advanced Engineering Mathematics
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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(a) Show that if two points. T P (P₁, P₂). Q (9,19₂) with Pr. pr. 9, 192 € Q the equation of the line through P and Q is of the form then ax+by =c with a, b, CER. (b) Derive from part (c) that if a line has two rational points, it has infinitely many rational points. P and Q have rational coordinates
Transcribed Image Text:(a) Show that if two points. T P (P₁, P₂). Q (9,19₂) with Pr. pr. 9, 192 € Q the equation of the line through P and Q is of the form then ax+by =c with a, b, CER. (b) Derive from part (c) that if a line has two rational points, it has infinitely many rational points. P and Q have rational coordinates
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