Unknown
Answers to Exercises; Chapter 4 303 When x < -2, 0 < 4x2(2x2 - 1) < 8x4 - 4x2 - 3x + 3 < (3x2 - I)~; when -2 < x ...
304 5.2. (f) Answers to Exercises and Solutions to Problems 1 +r+r2 -15 + -15 - 5 5.3. (b) The quadratic has a single zero o ...
Answers to Exercises; Chapter 4 305 I I I r>l 5.4. I I D, r<l 0 6 DI D2 ...
306 Answers to Exercises and Solutions to Problems 6.1. Let mi be the multiplicity of the zero ti. We have that p(t) = (t - tl)m ...
Solutions to Problems; Chapter 4 307 2(n - m) of the a;. Suppose the former occurs. Then either g(t) - 1 or g(t) + 1 must vanish ...
308 Answers to Exercises and Solutions to Problems For there to be infinitely many solutions, it is necessary that a = -2c and b ...
Solutions to Problems; Chapter (^4 309) (Note that u(u + v) = 1 - b, being the sum of the zeros of p(t) - t.) Hence, two zeros o ...
310 Answers to Exercises and Solutions to Problems 8x6 - 9x3 + 1 = 0, whence x3 = 1 or l/8. The solutions (x, y) are (O,O), (9/8 ...
Solutions to Problems; Chapter 4 311 Checking the possibilities leads to (x, y) = (2,2), (-2, -2), (3, l), (-3, -l), and four ot ...
312 Answers to Exercises and Solutions to Problems Suppose that u = VW. Substituting for w in (2) leads to v2 = 1, and we get th ...
Solutions to Problems; Chapter 4 313 8.14. From the last two equations (y + %)2 h (y - z)2 + 4 y% = 914 - 3x + x2 + 314 = x2 - 3 ...
314 Answers to Exercises and Solutions to Problems whence vy(y - x) = c - bx vy2(y - x) = d - cx (c - bx)2 = (b - ux)(d - cx). T ...
Solutions to Problems; Chapter (^4 315) whence ux = (x-y)(x-z), by = (y-x)(y-z), cz = (z-x)(z-y). Hence ax(z - y) = by(x - z) a ...
316 Answers to Exercises and Solutions to Problems 8.22. First solution. Clearly 0 < x < y. If x 5 1, then (x + y)” > 9 ...
Solutions to Problems; Chapter 4 317 () yields (u - 3)(3u3 + u2 - 4u - 12) = 0. C onversely, any solution of this equation leads ...
318 Answers to Exercises and Solutions to Problems sphere and at the center of the circle of intersection, it must intersect thi ...
Solutions to Problems; Chapter (^4 319) squares of the lengths of AP, BP and CP, where P is any point distant 4, &, fi from ...
320 Answers to Exercises and Solutions to Problems The roots of x3 +px2 + qx + r = 0 are vertices of an equilateral triangle iff ...
Solutions to Problems; Chapter (^4 321) The result can be generalized to polynomials of degree n. See Problem 4426 in Amer. Math ...
(^322) Answers to Exercises and Solutions to Problems and those of p(t) + 1 and q(t) + 1 be ~1,... , v,. Clearly, the Ui are dis ...
«
12
13
14
15
16
17
18
19
20
21
»
Free download pdf