check R3 is reflexive,symmetric, transitive
R3 on R defined by (a,b) belongs to R3< => a2-4ab+3b2=0

R3=a, b: a2-4ab+3b2=0For any aR, we havea2-4a2+3a2=0a, a R3 for all aRSo, R3 is reflexive.Let 3, 1R3 . Thena2-4ab+3b2=9-4×3×1+3×1=9-12+3=0But, for 1, 3R3 a2-4ab+3b2=1-4×1×3+3×9=1-12+270So, R3 is not symmetric.Let 3, 1, 1, 13R3 But, for 3, 13R3 a2-4ab+3b2=9-4×3×13+3×19=9-4+130So, R3 is not transitive.

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