Download Homework (due Thursday 13/9) 1. Simplify the following

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