9515746005

c) 5x + 3y — 13 = O, x - 1 = O, 4x + 3y - 12 = O, d) x — y + 7 — O, 2x - 3y + 4 = 0. x-2y-3 = 0. 4.7. (-5,-4).

5.1.    a) S(-l,l), r = 2, b) S(1,0), r = 1, c) S(-l,§), r = |, d) S(-1,-1), r = f. 5.3.

a)    (x - 2)² + (y + 3)² = 10, b) (x - 3)² + (y - 4)² = 25. 5.4. (x - l)² + (y + 3)² = 68. 5.5. (x + §)² + (s,-2)² = f.

6.1.    x² - 16x + 16. 6.2. a) (§,-j), b) (|,|). 6.3. a) a: £ {-5,5}, b) x £ {-7,0}, c) x £ {|, l}, d) X — 3, e) x £ {—a/2, —1,1, \/2}, f) x £ (—co; —4] U [4; oo),

g) x € (—oo; 1) U (3; oo), h) x G R, i) x G [—3,2]. 6.4* —1. 6.5. x⁴ — 10x² + 1. 6.6. k = 5, l = 3,m = —2. 6.7. a) x² + 2x — 3, b) 3x³+x² — 5x+4. 6.8. a) iloraz x³ — x²+3x — 3, reszta 5; b) iloraz 2x² + 3x+ll, reszta 25x —5. 6.9. a) x = —2, b) x G {—1 — \/5, —2, —1 + \/5)5}, c) x € {-4, -2,4}, d) x = 1. 6.10. a) x € [2; 3] U [12; oo), b) x € [2; 3] U {-1},

c)    x € (—oo; — 1)U(1; oo), d) x € (—oo; —1]U{2}U[3; oo), e) x € [—3; —1]U{2}, f) x € [0; 2], g) x 6 (—oo; —3) U (—2; 2), h) x € (2; oo).

7.1.    a) A = (-5; -1] U (3; oo), B = (-oo; -2] U (1; 2] U (4; oo), A\JB = (-oo; -1] U (1; 2]U U(3;oo), Ar\B = (-5; —2] U (4;oo), A\B = (—2; -1] U (3;4], B\A = (—oo; —5] U (1;2], A' — (—oo; —5] U (—1; 3]; b) A = (—oo; —1) U (1; oo), B = (—oo; —1) U [0; 1], A U B = = (-oo; -1) U [0; oo), A n B = (-oo; -1), A \ B = (1; oo), B \ A = [0; 1], A' = [-1; 1],

7.2.    a) D, = R \ {—1,0}, b) D, = R \ {5}, c) D_h = (—1; ŁaH] U [^; oc).

7.4.    a) x = i, b) * £ {1 (l — S) , 1 (l + V5)}, c) x = -|. 7.5. a) x £ (-1; 1),

b)    x £ (—oo; —2) U [—1; oo), c) x £ (—oo; |j.

8.1.    a) 4, b) 12, c) 2, d) 2, e) y, f) 1,2, g) §. 8.4. a) x = -1, b) x = |, c) x € {0,1},

d)    x = -3, e*) x =    8.5. a) x G [—1; 1], b) x G (— \\ |), c*) x G (3;oo), d*) x G (-oo; 1],

e)    XG [0; |).

9.1.    a) 3, b) c) 8, d) -3, e) -i, f) -4, g) 14, h) -f, i) 4900, j) f, k*) j, 1) 2. 9.2.

9.5.    a) x = log₃4, b) x = |, c) x = ±2v^2, d) x = 9, e) x = 4, f) x G ||, 9}, g) x G {1, \/3}-

9.6.    a) x G (0;9), b) x G (—1;7) \ {3}, c) x G (—oo;0), d) x G (l;oo), e) x G (1;5],

f)    x G (—oo; —1) U (5;oo), g) x G (0; 1] U [2;oo), h) x G (l;oo), i) x G (—oo;0] U [log₆5; 1).

9.7.    a) D_f = (-2; 2), b) D_f = [3; oo), c) D_f = (-2; -1) U (-1; 5), d) D_f = (-1; 0] U [2; 7].

6.1. x² - 161 + 16. 6.2. a) (|,-j), b) (§,*). 6.3. a) x £ {-5,5}, b) x £ {-7,0},

c)    x £ {1, l}, d) x — 3, e) x £ {—s/2, —1,1, \/2}, f) X £ (—oo; —4] U [4; oo),

g)    x £ {—oo; 1) U (3;oo), h) x e K, i) x £ [-3,2], 6.4." -1. 6.5. x“ - 10x² + l. 6.6. k = 5, l = 3, m = —2. 6.7. a) x² + 2x —3, b) 3x³+x² —5x+4. 6.8. a) iloraz x³ —x²+3x —3, reszta 5; b) iloraz 2x²+3x + ll, reszta 25x —5. 6.9. a) x = —2, b) x G {—1 —\/5, —2, —1 + \/5,5}, c) x G {-4, -2,4}, d) x = 1. 6.10. a) x G [2; 3] U [12; oo), b) x G [2; 3] U {-1},

c) x G (—oo; —l)U(l;oo), d) x G (—oo; —l]u{2}u[3; oo), e) x G [—3; —l]u{2}, f)xG [0; 2], g) x G (—oo; —3) U (-2; 2), h) x G (2; oo).

7.1.    a) A = (-5; -l]U(3;oo), B = (-oo;-2] U (1; 2] U (4; oo), AU B = (-oo;-1] U (1; 2]U U(3; oo), A n B = (-5; -2] U (4; oo), A \ B = (-2; -1] U (3; 4], B \ A = (-oo; -5] U (1; 2], A' = (-oo; -5] U (—1; 3]; b) A = (-oo; -1) U (1; oo), B = (-oo; -1) U [0; 1], A U B =

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