# HF6_megoldas

## 1579 days ago by ballar

X = matrix([[x,1],[1,x]]); Y = matrix([[2,x],[-1,-1]]); Z = matrix([[-1,2],[x,2]]); A = block_matrix([[X,X],[X,X]]); B = block_matrix([[X,Y],[Y,X]]); C = block_matrix([[X,Z],[Y,Z]]); xa = Set(RR).difference(Set(solve(det(A) == 0, x))); xb = Set(RR).difference(Set(solve(det(B) == 0, x))); xc = Set(RR).difference(Set(solve(det(C) == 0, x)));
xa
 Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == r1} Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == r1}
xb
 Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == -2, x == 1, x == -1/2*sqrt(17) - 1/2, x == 1/2*sqrt(17) - 1/2} Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == -2, x == 1, x == -1/2*sqrt(17) - 1/2, x == 1/2*sqrt(17) - 1/2}
xc
 Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == 1/2*sqrt(17) - 1/2, x == -1/2*sqrt(17) - 1/2, x == -1} Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == 1/2*sqrt(17) - 1/2, x == -1/2*sqrt(17) - 1/2, x == -1}
plot(det(C),(x,-3,2)) [(a,b,c) for a in range(1,100) for b in range(a,100) for c in range(b,100) if a^2 + b^2 == c^2 and (is_prime(a) or is_prime(b) or is_prime(c))]
 [(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), (11, 60, 61), (12, 35, 37), (13, 84, 85), (20, 21, 29), (28, 45, 53), (39, 80, 89), (48, 55, 73), (65, 72, 97)] [(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), (11, 60, 61), (12, 35, 37), (13, 84, 85), (20, 21, 29), (28, 45, 53), (39, 80, 89), (48, 55, 73), (65, 72, 97)]