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Homework (due Thursday 13/9) 8. Solve the following equations/inequalities of order > II: (a) 3x4 − 7x2 + 2 = 0 (b) 3x3 + x2 − 19x + 15 = 0 1. Simplify the following expressions: q q 3 4 5 (a) 8 x 8y · 8 64x y2 q q 4 27c2 a3 b2 · (b) 2 3c a2 b 2. Factor the following expressions: (c) (2x2 − 1)(x2 − 3) > 0 (d) (2x − 7)(x2 − 9)(1 − x3 ) ≥ 0 9. Find the domain D of the following rational equations/inequalities and solve them: x−3 4 (a) 3x+5 x+2 (a) 2ab − 2ac + 3bx − 3cx (b) 2 (2x+1)2 (b) 25x2 − 25 xy + (c) (x−1)2 +7 x+2 3 1 2 16 y 2 2 4 (c) 8x + 12x y + 6xy + y 5 4 3 (d) 4x − 8x + 6x − 12x 6 (e) x5 + 2x4 − 6x3 − 8x2 + 5x + 6 3. Solve the following I order equations/inequalities: (a) x−3 6 +2= x−2 3 + 1 6 (b) (2 − 3x) − (3x + 1)(3x − 1) + 1 = 3(x − 1) − 15x (c) (d) (x−1)2 2 +x−3 − > x+1 3 x+1 2 − 2 (a) (c) (d) 1≥ x2 −1 4 4. Solve the following I order equations/inequalities in x, describing solutions for varying real parameters a, b, k: (a) x(3 − 5a) + 3(a − 1) = (a − 1)(a + 1) − 2ax x −1 1−4x2 + = 7x−2 2x+4 2−4x (4x2 −1)(3x+2) ≤0 (e) (f) √ x2 + 3x + 9 = 3 √ x−4= 3−x p 3(x2 − 1) < 5 − x √ 3 x2 − 28 + 3 ≤ 0 √ 2x + 5 ≥ 3x + 7 √ √3 x+7 ≥1 11. Solve the following equations/inequalities with absolute values: (a) 2|x + 4| = 1 (c) a(x + 2) < 1 + 2ax (b) 2x − 1 > |x − 3| + x (d) kx − k(2x − 1) = (1 + k)x + 3k + 1 (c) 2x − 1 > |x − 3| + |x| (e) k(x − k) > 3(x − 3) (d) |x| − 2 < |x + 1| 6. Solve the following II order equations/inequalities: (a) (x + 2)2 = x(x + 12) (b) (3x − 1)x ≤ (3x − 2)(8 + x) (c) 2x2 + 2x − 5 + x > x2 − 2 + 3x + 1 7. Solve the following II order equations in x, describing solutions for varying real parameter k: (a) x2 + 2kx − k + 3 = 0 (b) 2kx2 − x + 1 = 0 (c) (2k + 1)x2 − 2(2k − 1)x + 2k + 1 = 0 1 (3x+2)(2x+1) ≤2 (b) (a + 3b)x + a = b − (2b − a)x 5. Solve the following systems in one or two variables: ( 3x − 1 > 2 (a) −x + 2 > −2 ( 3x + 2y + 1 = 0 (b) x−y−3=0 2x − 3 < 0 (c) −x + 4 > 0 2 x + x − 12 = 0 = 10. Find the domain D of the following irrational equations/inequalities and solve them: (b) 2 1 2 (d) 2 2 − (e) |(x + 1)2 − x(x + 4)| > (x + 1)2 − x(x + 2) + 6